The Ghanaian midfielder was most recently on loan with Partick Thistle following spells with Watford and Carlisle after leaving Dundee United in 2011.
Head coach Robbie Neilson told Hearts News: "It's great that Prince has put pen to paper. He's been at training for the last two weeks and he's played a few games for us.
"He's looking good and he's a top player. He's played in the SPL for a long time and he's played in England at a very high level so I'm pleased to get him.
"He gives us a bit of strength in there. We've got some good options now in the middle of the field. He's a good character as well.
"He hadn't done a pre-season after he finished up last season so I just wanted to see where he was and he's a fit guy.
"If this is the condition he's in, having only trained for just over a week, then I'm looking forward to seeing what we can get out of him in two or three weeks' time."