Defender Wootton, 21, joins until the end of the season having enjoyed a previous loan spell at London Road.
He was kept out of the side by Ryan Bennett and Gabriel Zakuani last time round but Zakuani's involvement in the African Cup of Nations is likely to give him his chance.
"Scott was very unfortunate last time he was here because Ryan Bennett and Gabriel Zakuani struck up such a good partnership, but this time, I am looking for him to be a regular starter," Posh boss Darren Ferguson told the club's official website.
"He has played in a three-man defensive line before and he is very comfortable in any of those positions. I am really pleased to get him, he has been a big part of the squad at United and they think very highly of him.
"We have got him until the end of the season. It is an area I wanted another body in because obviously Gabriel is away with the African Cup of Nations."
Midfielder Petrucci joins on a one-month loan deal. The 21-year-old is set to stay with the club until February 9 but Ferguson is hopeful of extending the spell should it prove a successful one.
"Davide is a very good footballer, is a good size and this is his first loan move, so that is why it is only for a month but, between the two of us, I am sure we can extend it to the end of the season if it works out for all parties," he added.
"He can play anywhere in midfield, he can play off the front and he could play in a sitting role. He is a very talented boy and we will just find the right position for him. Lee Tomlin is obviously suspended, I have young Jaanai Gordon who has impressed, but I think Davide can play in that one off the front role."
He added: "We need bodies in, I spoke to my Dad (Sir Alex Ferguson - Manchester United manager) about Davide for a couple of weeks and there was other clubs in for him so we are delighted to get him to the football club. My Dad was happy for him and Scott Wootton to join and they will go into the squad for Saturday."