The 22-year-old has signed a four-year contract with the club to 2021 with the option a further 12 months and will formally be registered as a United when the transfer window officially opens on 1st July.
United had announced over the weekend that a fee, believed to be £30m rising to £35m, was agreed with Benfica. Lindelof later arrived at United's Carrington training base on Wednesday morning after international duty, undergoing a medical and ironing out the finer details.
"I am thrilled to be joining Manchester United. I have enjoyed my time at Benfica enormously and I have learned a lot there," the player told Man Utd.com.
"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," he added.
Mourinho himself said, "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."
A move for the promising centre-back, who becomes the second most expensive Swedish footballer of all time after Zlatan Ibrahimovic, has been on the cards for a number of months after United pulled back from an initial deal to sign him in January.
There were complications regarding a sell-on payment between Benfica and his former club Vasteras SK at the time, while Jose Mourinho also ultimately opted against making changes to his squad mid-season.
Despite his young age, Lindelof already has Champions League experience and tasted domestic glory with Benfica after capturing Primeira Liga titles in each of the last two seasons, as well as three domestic cups since first moving to Portugal in 2012.
It is expected Lindelof and Eric Bailly will be United's primary centre-back pairing in 2017/18.
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