So my players backstory is that of literally something based off of revenge. His goal is to kill his main enemy for all the evils he did to him. And literally, it feels just perfect to secretly make him a revenant. So if this is a good idea, then how would that work? If this is not a good idea what is the limitation of DM's agency, because personally I want to do this, but I also don't want my player feeling like his character has been taken from him. 

You can talk with them about it. Ask them something like “would you want your character to have some sort of mystical tie to their enemy related to revenge? It would have some benefits and probably be cool, but it will likely have some downsides.”

If the player still isn’t sure, but is interested, consider asking them outright, and having their character not know. They could help with the RP, like swearing to “kill (Fred) no matter what, even if it kills me!” without realizing how literal that oath is.

I don’t know exactly how you would run it mechanically, but make sure they know that it could have major RP and sometimes mechanical consequences to the choice.

I would second the Ask your player if that is something they would be okay with. there are also ways to have something similar without actually making the character a Monster. For example, being a Reborn race, Having the Hollow One Feature from the critical role book, Playing a Zealot barbarian that refuses to die until they get their revenge.

The biggest thing for me is not necessarily taking away the player's agency, but how to mechanically represent that without being unfair to the other players. If this player gets free things on top of being a player character that is not fair to the others, if the player is just directly a Revenant then they are going to be much stronger than the other player characters and not get the dynamic parts of growth that a player character does. If you want to make some special combination thing, then that is fine but also seems really complicated and could get very messy very quickly and again would be unfair to the other players if a single player got something special like that. 

On the Mechanics, maybe you're all aware but it was new to me when I stumbled not long back across this UA proposing a Revenant player race.  

I'd say the whole relentless/undying thing may well torque some of the other players in the group.  For Devils advocate supporting the option, I'd say the tradeoff is the PC being relentlessly monomaniacal loses a lot of player agency since all its deeds (at least according to my take away from the MM) are supposed to be in service of the vengeance drive.  "No side quests for you!" There's also the fact that once vengeance is achieved and the PC "wins" they're dead.

What about throwing a triple twist in there?

The player is told their character is a revenant. They receive information on the whereabouts of the bad guy, whenever possible, which will lead the party through the questline, like a revenant. The character has a fuzzy memory of the BBEG attacking them and "leaving them for dead", and doesn't know they are a revenant, but the player "does".

When they get to the BBEG and kill him, nothing happens. The "Revenant" character doesn't die, and they find out that they were being played by the real killer, who has planted false memories in their head of the other guy killing his family, replacing true memories of him killing them, and has been telepathically communicating with him to guide him to killing the guy, who the real killer wanted dead. The real killer then disappears, sparking a "find him and kill him" questline which is not necessarily the main plot any more. The player no longer thinks they are a Revenant, just a poor fool who got played.

As the player focuses on their revenge again, they start to get feelings as to where to look. They get insight rolls each day which tell them information about the real killer. They track him down, and when the player gets to the final fight, you tell them that they feel nothing but the burning desire to kill this person.

When they kill the person, their true memories are revealed by the DM, and the character does indeed die, as they were genuinely a revenant. Their quest was to kill this guy, but it was corrupted by the true killer and they followed the wrong guy - which is why they survived killing the first one.

Summary, using names to say "guy" less!:

the timeline of PC, Bob (the BBEG), and Dave (the real killer):

1: PC's family is killed by Dave, who also kills PC.
2: PC rises as a revenant, and Dave captures them, thinking they just survived and not realising they are a Revenant, and corrupts their memories, so they remember Bob killing their family instead of Dave.
3: PC goes off for single-minded revenge against Bob, guided by telepathic voices from Dave, who is trying to convince PC that he is a revenant, which Dave thinks he isn't and which he actually is.
4: PC kills Bob, and nothing happens. Dave reveals his hand and thinks he can just escape PC, disappearing away.#
5: PC starts tracking Dave, and gets information about where he is. Player might use or suspect this info, after what happened, but this info is the real deal for Revenant-dom.
6: PC finds Dave, and learns at the fight (from a flashback) that his is a revenant and Dave is his target.
7: PC kills Dave (all going well) and collapses dead, job done.

7 (Alternative): PC kills Dave and falls dead. The god of Vengeance appears to him and congratulates him on a job well done, and offers him a chance to be reborn as his servant. PC can choose to die or take next 3 levels as Paladin, to Oath of Vengeance (if not already) and serve the God of Vengeance, who will whisper targets to him for him to avenge himself on - perhaps all the lieutenants and such of the bad guy, who helped the murder happen.

This would all need player buy-in for the "you win, you die" aspect of it. The player would need to be willing to kill their character off for the story. If they buy in, you can enjoy the ride as they think they're going to die, then think they're not going to die, then think they're going to die again, then (if you take the alternative ending) they get an offer to live. Be sure to tell them that they get no plot armour and can simply fail at their vengeance if they are killed en-route!

I know it feels cool to surprise the player with this, but 99% of the time this is a terrible idea. Players get to design their characters, so unless the player has expressed to you the desire for surprise (I had this happen once), then it needs to be up to the player if his/her character is a revenant. There are all kinds of implications of being such a creature, including that they are undead, but also, that after they get revenge they "die" for real, and so on. Your player needs to be on board RPing this.

So... I know this feels like spoiling the surprise but being a Revanant is not just something like, your character is not really a pauper but was of noble birth. I would not do this to a player unless they asked for a big reveal/surprise. And probably not even then, with something like a Revenant. My considered advice is to ask the player, "Would you like your character to be a revenant -- maybe he doesn't even know himself yet?" See what the player says.

Could it work? Yes, but the shock value of revealing it as a twist isn’t worth the potential disappointment for the player, so discuss it with them first, obviously. And having a character so bent on one goal either forces them to justify why they’re on unrelated quests or forces you to build the storyline around them, annoying other players with less screentime. So while it’s definitely possible, it’s not as easy as it might seem. If you’re not deterred, talk to the player about it, and be as up front about what it entails as you can.

As for mechanics, don’t give any special bonuses or penalties (statistically, storywise is fine). Especially not automatic resurrection. That’s just a recipe for angry players.

I have talked with the player. He was extremely enthusiastic about the idea, and we both agreed that he will not gain any of the revenant stats. This will be very fun and interesting to setup.

I'd talk to the player.  I know...I know...this is an amazing original thought.

OK, if the player is enthusiastic then you are good.

Most people in this thread are missing the word "secretly" in the OP's post. I believe that the DM is asking whether it would be OK to spring on the player mid-campaign that they are a Revenant.

If you agree with the player, then it's fine. If you agree with the player that there will be a big mystery to solve about the character, then that's also fine.

But because you've suggested it as a secret, the answer is a categoric No. You should not, under any circumstances, change essential or key details about a player character without a player's permission. The character is what the player gets to create and to control. The thing that you shouldn't change is core details of a player's ability to play their character.

You can put in discovery storylines for characters if the player is willing to take one on. But you should not do this secretly. I ask each of my players to come up with a mystery about their character that they don't know the meaning of, and that they will trust me to develop with them. For example, one of my current players was washed up on the shore as a baby with a burn on his face and wrapped in a torn red cloak. He doesn't know any more than that. But he has created it to be open ended, as a long-running storyline that will develop with the character. Over time, this character has seen a time-travel vision of himself on a ship that catches fire in a deadly battle, and will later learn more about what he actually is. But this is done with the player's express permission.

Just ask. Without saying specifically what you have in mind, ask the player if they would be okay with you introducing major twists into their backstory. Ask if there is anything they would consider off-limits for you to add.

Quote from Cindrellic >>

I have talked with the player. He was extremely enthusiastic about the idea, and we both agreed that he will not gain any of the revenant stats. This will be very fun and interesting to setup.

That's always great when a player is happy to go along with this sort of thing! How are you going to set it up for them?

I have something figured out. First his archnemesis is a Ranger - Drakewarden (UA). So, his main archenemy is a Hobgoblin clan, and the main leader of that clan. Over course of a bunch of time they fought in a stalemate when suddendly his archnemesis is way stronger and kills all his friends and family. He then goes wandering around in a self-imposed shame exile thing. His backstory is actually super cool but that is a WAY watered down version.

So here is what I plan to do: 

I had already planned on having the Hobgoblin nemesis being way stronger to the fact that he made a pact with the main BBEG of the whole campaign so, if the PC and the Hobgoblin met up again, his powers would be stronger. Now what I have planned is since the Hobgoblin got much stronger, he is going to actually be the one who revived him. (This hobgoblin is an ego-tistial maniac, and so its perfect during the time when he killed all of his family and friends he also killed the PC, then to show even more how powerful he was, he revived the PC, just to play with him.) So now if the PC kills his nemesis the Hobgoblin, he kills himself, because his lifeline is tied to the Hobgoblin. (Thats the way how I am making this kinda "revanant" thing, I know he was revived, but the player thought it would be cool if the Hobgoblin revived him. So I agreed.) So I would run a quest line of the party having to retrieve the old body of the PC and have the spirit of the revived PC go back into his old body so that he can not be tied to the Hobgoblin. (That part is ruff, how could I have the connection severed between the Hobgoblin??) The PC does not know in game that he is revived, and the player is a great RPer, so I'm really excited to see how he does.

But that is it so far. Let me know for new suggestions seeing the whole "inhabit old body" just sounds like a confusing headache.

That's a good way of going about it, I like that.

Having the PC cloned for the Hobgoblins enjoyment works well to my mind. In so far as recovering the original body and then transferring the soul across, this has a huge amount of potential for some sinister and devious stuff!

Firstly, have the place where they need to go to transfer his soul be an abandoned and sinister place, infested with zombies and skeletons (you know, necromancer stuff). Have the party assured that the necromancer, who was believed to be a servant of the trickster god, disappeared long ago, but they never cleared out his citadel, instead content to just seal it up. The building is charred from an attempt to burn it down, but it survived without structural damage. The building is full of tricks etc, because of his ties to the trickster god.

When they have fought their way in, they can find the twin alters needed to transfer the soul from one body to another. They perform the ritual, moving the soul from the live body to the dead one, who returns with 1hp.

Then, unexpectedly, the first body sits up. It looks around, looks at its hands, and smiles. "Yes, this will do." He seems fairly amiable, and doesn't attack the party. If the party attacks him, then they will find that this is in fact the trickster god himself, who had been imprisoned by the necromancer but has now inhabited this body. He toys with the party for a bit before teleporting away (they won't be able to hurt him properly, though they might have some tricks which can deal some concern to him).

The Trickster god is now in an interesting position; They are basically untouchable because of their powers, and can wreak merry havoc for the resurrected PC by imitating him and getting him involved in all sorts of things, such is the way of a trickster. But, if the Hobgoblin dies, so does the Trickster, because of this bond that was made. You could have him kidnap the Hobgoblin to keep him safe, or just try to hinder the party, or try to persuade, bribe or blackmail the party into not killing him - whatever works in your world. He could become an interesting sideline which is snuffed out when the hobgoblin is killed, but might leave behind arrest warrants and all sorts for the PC to deal with!

This is something you have to talk about for sure, depending on how much your players trust you and you trust them DM agency can grow.

As an example I DM and one of my players has his own campaign that I play a Paladin in, I told him before we started that if I stray from my oaths to make me an oath breaker no questions asked(normally some warnings would happen in our games). However this is only one of my 5 players that have this level of trust its something you work towards and respecting their character arc is important.