The 47-year-old was confirmed as David Weir's successor on a contract until the end of the 2015-16 season at a press conference this afternoon.
Clough said that once stability has been found, the goal with the Blades is to get promoted back to the Championship.
He told reporters: "I am proud and honoured to come here.
"I will try to build a team and a squad to get promoted. The target is to get stability and a squad together to push for promotion."
Clough's first game in charge will be at home to Crewe Alexandra on Saturday.
He takes over with the club in League One's relegation zone on nine points from 13 games.