United had a £100,000 bid for the player accepted by Hull City at the beginning of May, but he turned down a move to Glanford Park.
That raised interest in the 27-year-old's signature, with Rovers beating Bristol City and Chester to him.
The transfer fee has not been disclosed, but it is unlikely to be as high as that offered by Scunthorpe.
Rovers boss Ronnie Moore said: "This is a great signing for the club and I would like to thank the chairman for doing the deal.
"Kevin had the opportunity to go to Bristol City and Scunthorpe but he's a local boy who wants to play at Prenton Park and it says a lot for Tranmere Rovers that we were able to pull him in.
"I am looking forward to working with Kevin and he will be a great asset to the side. He will give his all and hopefully steer us in the direction we want to go."