Bennett, who joined United after their promotion to the Premier League in 2006 as cover and competition for Paddy Kenny, made more than 500 career appearances as a player, also turning out between the posts for Birmingham City.
Rovers boss Gary McSheffrey described the appointment as “a real coup” for the League Two new-boys.
“We were aware he became available,” McSheffrey said, “and had an initial chat a few weeks back. It was nice to get him in.
“Getting someone of Benno’s experience to work with the first team is so key for the club. It shows the players we mean business.
“He knows the game inside and out.”