Recording breaking transfer for Manchester United new boy Pogba
Having left United for Juventus for £1.5m in 2012, the 23-year-old midfielder returns after four years away.
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, including 5m euros if Pogba signs a new contract.
It surpasses the past £85m transfer fee that Real Madrid paid Tottenham for the Wales forward Gareth Bale in 2013.
The announcement was made by United on Tuesday, with Manchester United posting a video showing the player - with a red devil marked into his hair - emerging from the shadows.
Just how good is Pogba?
◾Former France striker Thierry Henry believes he can go on to become "one of the best in history" while fellow World Cup winner Patrick Vieira described him as an "extraordinary player" and said it was a "mistake" for Manchester City not to sign him from United
◾Ryan Giggs, United legend said Pogba "has got everything"
◾France legend Zinedine Zidane thinks Pogba is a "complete player"
◾Juventus coach Massimiliano Allegri said in May 2015 that Pogba "needs to stop showboating in midfield" and that he makes "avoidable" mistakes
◾Arsenal manager Arsene Wenger claims Pogba is in a "maturing period" and will not find his best form until the age of 26
◾Former England striker Gary Lineker said during Euro 2016 if he was "the world's most overrated player"
◾Ex-United midfielder Paul Scholes had questioned Pogba's £89m valuation, saying he was "nowhere worth that kind of money yet"