"This is a blow because Garry's Premiership experience would have been invaluable to us next season," Blades manager Neil Warnock told his clubs official website.
"The player himself had always maintained that we would see the best of him in August after a full pre-season programme."
Flitcroft made almost 250 appearances for Rovers follwing his signing from Manchester City for £3.5million in 1996.