Pearson, 20, who spent time on loan with Barnsley last season, and Rothwell, 20, will both stay at Oakwell until January 3.
Barnsley head coach Lee Johnson told the club’s official website: “Ben really impressed me last season – both when he played against and for me.
“He is a tremendous talent with energy to burn and is a good passer of the ball. He will be an asset in our midfield and I’m really looking forward to working with him again.”
Pearson made 22 appearances for Barnsley during his stay from January until the end of last season, while Rothwell made three appearances during a loan spell at Blackpool.
Johnson added: “I’m really excited to have Joe on board as well as Ben.
“We are very lucky to have two highly-rated midfielders on our hands and I’m really grateful to Manchester United for allowing us to bring them both here.”