Paul Pogba said "the time is
right to go back to Old Trafford" after completing his world-record £89m
transfer to Manchester United.
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 £85m that Real Madrid paid Tottenham for Wales forward Gareth Bale in 2013. The announcement was made by United just after 00:30 BST on Tuesday, 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 and grime artist Stormzy, whose most successful song to date is 'Shut Up'.
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It will be the first time in 20 years an English club has set a world-record transfer fee, after Newcastle United paid £15m to sign England striker Alan Shearer from Blackburn Rovers. Pogba joined United from French club Le Havre in 2009 as a 16-year-old, but made just a handful of appearances before his contract expired in July 2012.
He has made 178 appearances for Juventus, scoring 34 goals, and helped the club reach the 2015 Champions League final. The Serie A side had offered him a new contract, while Real Madrid were also interested in signing him.
Pogba said his mum told him he would return to Old Trafford and that it was his "destiny". Speaking to MUTV he added: "I just came back to Carrington. It was like I'd just come back home. I just went for a holiday."
Pogba said he had spoken to Mourinho "a few times", as well as talking to France team-mates who had worked under the Portuguese. "He gave me energy, he gave me positivity. They all told me he's the coach for me - he will make me improve a lot and make me work harder."
In a series of messages to Juventus supporters on social media, Pogba said: "Goodbye means nothing, it is the time we spent together that matters. I will bring with me a piece of you and leave you a little piece of me."