Wan-Bissaka has signed a five-year deal at Old Trafford worth £80,000 a week – a substantial hike from his £10,000-a-week contract at Palace.
United have paid £45m of the fee up front with a further £5m potentially coming in add-ons.
The transfer was delayed in the last few days due to a contract dispute Palace won, with a 10 per cent sell-on clause in place for the south London club should Wan-Bissaka leave United for more than £50m.
The 21-year-old was one of Ole Gunnar Solskjaer’s main summer targets, with the Norwegian manager keen to work with young, English talent.
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Solskjaer said: “Aaron is one of the best upcoming defenders in the Premier League. He has the right work ethic, talent and mentality to play for Manchester United and he fits exactly the type of player that we are looking to bring into the squad to help us improve and push on further.
“Aaron is a young, hungry player and eager to learn and that’s important at his age. I am delighted he has signed with us and we look forward to continuing his tremendous development so far.”
Ashley Young has one year left on his United contract and Wan-Bissaka is seen as the club captain’s long-term successor at right-back.
Wan-Bissaka started out as a winger but garnered attention at Selhurst Park after consistently thwarting Wilfried Zaha during a training session in 2016.
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No Premier League defender made more tackles than the full-back last term (129) while the Englishman was second in the league for interceptions (84).
United made an initial £40m bid earlier in the summer but Palace were determined to hold out for more, knowing United’s wealth and desperation to sign Wan-Bissaka.
The Croydon-born player was a United fan growing up and a picture of him sporting a Red Devils jersey in his youth was posted on his social media earlier in the week.
Wan-Bissaka is United’s second signing of the summer after Wales international Daniel James, also 21, who signed from Swansea for £15m.
The right-back becomes the fifth-most expensive player in United’s history after Paul Pogba, Romelu Lukaku, Angel di Maria and Fred.
Wan-Bissaka said: “It’s an unbelievable feeling and an honour to call myself a Manchester United player and something I know that only a small number of players have the privilege to say.
“I can’t wait to get going and integrated into the squad. I will have a short break now after the European Championships but I’m looking forward to starting training with the manager and my new team-mates on the pre-season tour.”