Blades boss Neil Warnock said "We think his experience and know-how will help other players. We are still hoping to add another striker to the squad before the weekend."
It was rumoured that Windass was attracting interest from two or three Division One sides, Coventry City being one of the interested parties, mentioned in the past few days.
Windass is the second Boro player to join a Division One side recently, after Jason Gavin joined Grimsby Town on loan for a month last week.