The 27-year-old has signed a contract which runs until the end of the current season.
After emerging through Nottingham Forest’s academy, Wallace enjoyed a short spell with Ilkeston before he was snapped up by the Blades.
He made 15 appearances for United under Clough before acquiring more game time on loan with Lincoln City and Fleetwood Town.
A versatile player who can be deployed in numerous positions, Wallace linked up with the manager again at Burton in 2019 following a stint at Matlock .
He recently returned to the club after a loan spell with York.
Clough said: “Kieran will provide us with good competition and cover in several positions, including midfield, left-back and centre-half.
“We’ve worked with him before and he performed very well for us in League One at Burton.
“He’s fully fit now after injury and will be a good addition to the squad. He’s ready to hit the ground running.”