Pogba has won 38 caps for France and the Serie A title with Juventus four times. Paul’s agent tweeted after the deal was done.
Paul Pogba said “the time is right to go back to Old Trafford” after completing his world-record £89m transfer to Manchester United.
The 23-year-old midfielder returns after four years away, having left United for Juventus for £1.5m in 2012.
Pogba, who signed a five-year deal, added: “This is the right club for me to achieve everything I hope to.”
Manager Jose Mourinho said the France international could be “the heart of the club” for the next decade.
United will pay the Italian champions 105m euros for Pogba, plus 5m euros (£4.5m) in performance-related bonuses and other costs.
It surpasses Wales forward Gareth Bale’s £85m move to Real Madrid from Spurs in 2013 as the biggest transfer deal in history.
The announcement was made just after 00:30 BST, with a glossy video showing the player – with a red devil marked into his hair – emerging from the shadows.
It was followed by a series of sponsor videos, including one with English rapper Stormzy.