British media said United splashed out a world record fee of 89 million pounds ($115.98 million) on the 23-year-old, eclipsing the 100 million euros ($110.84 million) Real Madrid paid for Welshman Gareth Bale from Tottenham Hotspur in 2013.
“I am delighted to rejoin United. It has always been a club with a special place in my heart and I am really looking forward to working with (manager) Jose Mourinho," Pogba said in a statement on United's official wesbite (www.manutd.com).
"I have thoroughly enjoyed my time at Juventus and have some fantastic memories of a great club with players that I count as friends. But I feel the time is right to go back to Old Trafford.
"I always enjoyed playing in front of the fans and can’t wait to make my contribution to the team. This is the right club for me to achieve everything I hope to in the game.”
Pogba is the latest of Mourinho's new signings following defender Eric Bailly, striker Zlatan Ibrahimovic and mid fielder Henrikh Mkhitaryan as the Portuguese coach revamps the under-performing squad he inherited from Louis van Gaal.
"Paul is one of the best players in the world and will be a key part of the United team I want to build here for the future," added Mourinho. "He is quick, strong, scores goals and reads the game better than many players much older than he is.
"At 23, he has the chance to make that position his own here over many years. He is young and will continue to improve; he has the chance to be at the heart of this club for the next decade and beyond."
The France mid fielder, whose strength and range of passing should allow United to play a more expansive game than the limited style adopted by Dutchman Van Gaal, has been a hot property all summer with Real Madrid also hovering.
"Everyone is interested in Pogba. He is a great footballer and when you are Madrid you always want the best," Real coach Zinedine Zidane had said before United wrapped up the deal for a player who scored 34 goals in 178 games for Juventus.
Pogba joined Juventus in 2012, having come through Le Havre's youth system before moving to United's academy in 2009.
He won four Serie A titles and two Coppa Italia trophies in a successful spell with the Turin club but was criticized after failing to shine in the 2015 Champions League final defeat by Barcelona and France's Euro 2016 loss to Portugal on home soil.
Pogba had signed for United on a three-year deal with a one-year renewal option which then United manager Alex Ferguson was keen to activate but the 18-year-old was frustrated by a lack of first-team opportunities at the club and decided to leave.
The Frenchman made just seven first-team appearances for United, all off the bench. "Ferguson came to my place. We talked. It did make me think. He wanted to keep me, but I'd made my decision to leave," Pogba has said.
He will now be reacquainted with Ferguson, who is a global ambassador at the club, but will take his orders from the uncompromising Mourinho who will demand a significant return on the club's world record investment in the Frenchman.
United have not challenged strongly for the Premier League title since Ferguson led them to the trophy in 2013 before ending his glittering 26-year reign as manager at Old Trafford.
Enter a name and e-mail address and we will e-mail this website link too them.