"Jennison is a player I've known about and admired for some time and up to about two years ago I would have said he was one of the brightest prospects in the country," Dundee United manager Craig Levein told his club's official website.
"Since then he's lost his way a bit through no real fault of his own and I'm delighted that we've managed to bring him to this club.
"He is a player who will not only excite the fans with his direct, quick running at defences, but he will also add pace to the team and strengthen our options going forward.
"He's still only 21 and I feel we can offer him the type of steady environment where he will now develop and fulfil his early promise.
"I'm excited about this signing and am sure he will develop into a real talent and a valuable asset for Dundee United."