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.
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Pogba, who helped hosts France reach the Euro 2016 final, has won the Serie A title in each of his four seasons at Juventus.
He is Mourinho's fourth signing at United, after Ivory Coast defender Eric Bailly, former Sweden striker Zlatan Ibrahimovic and Armenia forward Henrikh Mkhitaryan.
It will be the first time in 20 years an English club has paid a world-record fee - Alan Shearer's move to Newcastle United from Blackburn Rovers for £15m was the last.
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 has 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."
The summer's most protracted transfer
The move has rumbled on all summer, with the back pages of the newspapers featuring reports of deals done, deals delayed, counter-bids from big-club rivals, denials and intrigue over agents' fees.
At Mourinho's first Old Trafford news conference on 5 July he said he wanted to sign four players and had secured three. Many believed the fourth was Pogba.
But it has taken more than a month since then for the Portuguese to get his man.
On 9 July, United finally declared their official interest but there were rumours the player preferred a move to Real Madrid.
Following's France's Euro 2016 final defeat by Portugal, Pogba went on a long holiday to the USA.
His agent Mino Raiola said a number of clubs were interested in his client and continued to deny a deal with United had been agreed.
On Saturday, Juventus boss Massimiliano Allegri summoned Pogba to training, but just a day later United announced the player would have a medical - and on Monday he arrived in Manchester.
But it took until the early hours of Tuesday BST for the deal to finally be announced, a delay that Pogba called "annoying".
Writing on Instagram he said: "This transfer took so long because it was a huge decision and involved lots of thinking and work."
Why did Pogba leave Manchester United?
Pogba claimed he left the club "frustrated" and "disgusted" because former manager Sir Alex Ferguson did not play him.
Ferguson said he "distrusted" Pogba's agent, Raiola, and alleged an agreement with Juventus had already been made.
He gives his full reasons in the video above.
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 Vieiradescribed him as an "extraordinary player" and said it was a "mistake" for Manchester City not to sign him from United
- United legend Ryan Giggs 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 asked during Euro 2016 if he was "the world's most overrated player"
- Ex-United midfielder Paul Scholes had questioned Pogba's reported £86m valuation, saying he was "nowhere worth that kind of money yet"
Honours
- Under-20 World Cup winner and player of the tournament (2013)
- 4 Serie A titles (2013, 2014, 2015, 2016)
- 2 Italian Cups (2015, 2016)
- 2 Italian Super Cups (2014, 2015)
Most recent five times the world transfer record was broken
- 2013 - Gareth Bale £86m (Tottenham Hotspur to Real Madrid)
- 2009 - Cristiano Ronaldo £80m (Manchester United to Real Madrid)
- 2009 - Kaka £56m (AC Milan to Real Madrid)
- 2001 - Zinedine Zidane £46m (Juventus to Real Madrid)
- 2000 - Luis Figo £37m (Barcelona to Real Madrid)
Source: BBC Spor
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