The 47-year-old will take charge of his first game with the Blades against Crewe Alexandra on Saturday, less than a month after he was sacked by Championship side Derby County
Clough has been charged with the task of turning around United's flagging fortunes after David Weir was sacked earlier this month.
The Yorkshire club unveiled the 47-year-old former England forward as their new boss on Wednesday, less than a month after he was himself hired by Derby County.
He takes over a team languishing in the relegation zone but that have also picked up four points from their last two games - so the new boss will have something to build on.
Leaders Leyton Orient, meanwhile, will be looking to get back on track when they host Rotherham United after suffering their first defeat of the season against Coventry City in midweek.
Orient were beaten 3-1 by Steven Pressley's men but remain top of the table on goal difference as second-placed Peterborough United were held to a goalless draw by Sheffield United.
Darren Ferguson's Peterborough side have won five of their six away games in the league and they will be confident of securing another three points at Colchester United, having already beaten the Essex club 5-1 on their travels in the League Cup this season.
Elsewhere, Wolves closed the gap on the top two to three points with a 2-0 win over Oldham Athletic last time out and Kenny Jackett's side, who have a game in hand, travel to fifth-placed Bradford City on Saturday.
Fourth-placed Preston head to Notts County, while sixth-placed Walsall can make it three consecutive wins if they beat Coventry at the Bescot Stadium.
Bristol City's woes continued when they were beaten by Brentford at Ashton Gate on Tuesday night and they remain bottom of the table without a win ahead of their long trip to Carlisle United.
Elsewhere on Saturday, third-bottom Tranmere Rovers host Milton Keynes Dons, Stevenage entertain Crawley Town, Shrewsbury Town travel to Brentford, Oldham are at home to Swindon Town and Gillingham are at Port Vale.