Sharp joined Southampton from Doncaster in January, helping the Saints win automatic promotion to the Premier League with nine goals in 15 games.
But that step up to the top flight has prompted a reevaluation of the players needed by manager Nigel Adkins, and Sharp has been allowed to leave the club.
The move reunites him with Sean O'Driscoll, his manager at Doncaster, and pairs him with fellow former Iron player Henri Lansbury.