The former Liverpool and England winger, 45, was unveiled by the League One outfit last week and will be assisted by ex-Rovers midfielder Jason McAteer.
Barnes recently ended his short stint as head coach of Jamaica and was keen to return to club management.
He said: "I love football. I loved the part-time involvement with Jamaica, so to have the chance to work with players day in day out and influence them is really what I want to do.
"The type of manager and coach I am, I need every day involvement with the players because it's a simple but comprehensive way of playing."