The 22-year-old arrived at Manchester United’s Aon Training Complex on Wednesday morning after the two clubs agreed a fee which Press Association Sport understands to be 35million euros (£30.75million).
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.
Lindelof 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.”
Lindelof could be one of three or four high-profile acquisitions at Old Trafford this summer, with the club also understood to be keen on Alvaro Morata.
The Real Madrid forward’s agent said earlier this week that United had lodged a “very important offer” with the Spanish giants to try to bring him to the north west of England.