Wright is caretaker-boss Keith Downing's second signing since he was handed the role and he is expected to name the 36-year-old in the squad for Tuesday's Johnstone's Paint Trophy game against Swindon.
Downing told the club's official website: "Alan is a very good player and his career record speaks for itself.
"He will bring quality and experience to the team and I have received good reports on his character which suggests he will fit in with the way we do things.
"Alan has been training with Sheffield United and has kept himself very fit. He just wants to play some football now so it's a good move for all concerned."