On Wednesday morning, it was reported that Lindelof, who is believed to have cost Man United £31m, had arrived at the club's training ground to undergo a medical.
Lindelof's arrival has now been officially confirmed by the Red Devils, and the centre-back will make his debut on the club's pre-season tour of the United States next month.
"I am thrilled to be joining Manchester United. I have enjoyed my time at Benfica enormously and I have learned a lot there. But I'm looking forward to playing in the Premier League at Old Trafford and for Jose Mourinho," Lindelof told Man United's official website.
"I'm keen to get started and make my contribution to the team's efforts to win more trophies."
Meanwhile, Mourinho added: "Victor is a very talented young player, who has a great future ahead of him at United. Our season last year showed us that we need options and quality to add depth to the squad and Victor is the first to join us this summer.
"I know that our fantastic group of players will welcome him as one of us."
Lindelof, who is a 12-time Sweden international, joined Benfica from Vasteras SK in 2012, and initially represented the Portuguese side's B team, before stepping into the first-team picture in 2015.