Carver told the club website: "Alan comes with a wealth of experience as he has made only 500 appearances, mostly in the Premier League.
"He's got good energy and he will attack and go forward but primarily he is a defender."
Wright, whose last appearance for the Blades was against Arsenal on September 23, has played for many clubs including Blackpool, Blackburn and Middlesbrough as well as eight years at Aston Villa.