The 22-year-old arrived at Manchester United's Aon Training Complex on Wednesday morning after the two clubs agreed on a reported fee of €35 million (£30.75m).
United boss Jose Mourinho told the club's official website: "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 had arrived in Manchester fresh from international duty with Sweden, where he was an unused substitute in Tuesday night's 1-1 draw with Norway.
The Swede has been a long-time target for United as they look to bolster their defensive options ahead of next season's return to the Champions League.
He told United's official website: "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.”
"I'm keen to get started and make my contribution to the team's efforts to win more trophies.''
Manchester United are expected to make a few big signings this summer and Lindelof is the first among them with the club still being linked with the likes of Alvaro Morata and Andrea Belotti.
In defence, Mourinho now boasts an impressive array of options with Lindelof joining the likes of Eric Bailly, Marcos Rojo, Chris Smalling, Phil Jones and Daley Blind.
But Lindelof, who started his career with lowly Swedish club Vasteras before moving to Benfica in 2011, said he is happy to fight for his starting place.
In an interview with MUTV, Lindelof said: "Of course there are some great players here in my position.”
"I'm here to do my best to try to help the team as much as I can and it's always good to have other good players around you. When you have that, you get better as well.”
"I think every move means you have to adapt to a new environment but I feel comfortable in myself. I trust myself and it's going to be tough but I'm looking forward to it.”
"I always had a dream of coming here to play in the Premier League so, for me, it's a dream come true.''