The 23-year-old, who joined the U's from Everton in 2015, has signed a three-year contract with last season's League One champions.
"I've played against this club many times before and I've always been impressed. The song the fans sing before kickoff is amazing and I'm looking forward to having them on my side rather than against," he told The Star.
"I think the way United play and the way [manager Chris Wilder] likes his teams to go about their business will really suit me. I like to get on the ball, try and bring a little bit of composure but also dig-in for the people around me."
Lundstram has made more than 100 appearances for Oxford and has also spent time on loan with Doncaster Rovers, Yeovil Town, Leyton Orient, Blackpool and Scunthorpe United.