So, I think I'm kicking a player out of my game. That in and of itself is a long storyworthy of a Reddit thread, but I'll spare you the details here and just ask that you give me the benefit of the doubt here.

Thing is, this is a long running campaign and we are in the final quarter of it. I use a lot of customer content for my campaigns, and this player's character has some stuff coming up AND the other players in the party feel as though they need that character (Cleric) in the party still.

After some talk with the rest of the party, we have gotten another player lined up to take over the character. I'm gonna give him a full rundown of the story and the character so far, with the intent that he will take over. I also plan on letting him do some light rebuilding if he wishes. But, it's still a 15th-level character that has been through a lot and done a lot, and for the purpose of magic items alone it would be much easier if I could just reassign the character in the campaign to the new player, but I don't think I can rely or at least comfortably ask the original player to unassign his character so I can give it to the new guy; is there a way I can just do this as the DM?

Yes, if they are not going to willing leave the campaign, you can kick players out by unassigning all their characters and changing the join campaign link so they cannot just come back with the same link.

I recommend making a copy of the unassigned character, original copy for the kicked player and the new copy for the new player. No matter how awful a player is, I think it is still the right thing to do to return their character sheet back to them. To return the original copy, you can just make a temporary campaign and move the character sheet there, and have them kicked player join the temporary campaign to reclaim their character sheet.

While you can remove a player from a campaign, you cannot unassign a character from them. Only the player that controls the character can unassign it.

Ah, I see. I thought you could not remove characters unless they got unassigned first, but now I noticed a big old remove right next to every character without needing them unassigned/deactivated.

Ok but if I remove a player from the campaign, does it remove their character? So I won't be able to assign it to another player?

Removing a character does exactly as it says - it removes the character from the campaign (the Player version of this is Leave). It does not change the ownership of the character. As said above, only the account that owns the character (as in they have that character on their My Characters page) can Unassign a character when it is in a campaign - this then allows anyone in the campaign (including the DM) or anyone using the Join URL to claim the character.

If you are wanting the character or a copy of it, you are going to need to ask the player that owns that character to either unassign it, or ask them to make a copy and put that in the campaign/unassign it.