The 22-year-old midfielder has agreed a three-year contract to become Blades boss Nigel Clough's fifth signing of the summer.
"James is another good young midfielder to add to our ranks," Clough told the club website.
"He's had a couple of injury problems in the last 12 months but he was the driving force behind Tranmere's fine start a couple of seasons ago.
"James is one of the best midfielders in the league. We are delighted to get him; it adds extra competition for places."
Clough has also brought in Marc McNulty, Jamal Campbell-Ryce, Chris Basham and Andy Butler since the end of last season.