Summer signing Ji-Sung Park began the campaign as the club's official skipper, but an autumn injury saw Ryan Nelsen take over on an interim basis.
Nelsen has since announced his imminent departure for MLS side Toronto, and Hill has worn the armband this month despite Park's return to the squad.
Now Harry Redknapp has publicly backed Hill, telling the club website: "Clint is a great character, a good lad and a fantastic professional. He leads by example and has been superb for me since the moment I walked through the door.
"You know what you're going to get from Clint when he plays and that's 100%. He puts his body on the line for the club and that's what we need."
Hill said: "It's a very proud moment for me. I'm honoured and privileged. I'm sure it will be something I look back on in years to come with great admiration.
"Ji and Ryan have both had the honour of captaining the side this season and I'm relishing following in their footsteps."