transfer of Paul Pogba from Juventus for a world-record transfer fee of £89m.
The France international has signed a five-year contract and the 105m Euros fee will potentially increase through several add-on clauses.
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"I am delighted to rejoin United," said Pogba, who will wear the No 6 shirt. "It has always been a club with a special place in my heart and I am really looking forward to working with Jose Mourinho.
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"I have thoroughly enjoyed my time at Juventus and have some fantastic memories of a great club with players that I count as friends.
United will not pay Juventus' agent's fee, according to Sky sources
"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."
The 23-year-old left United for Juventus in 2012 having made just seven senior appearances in all competitions for the club, all from the bench.
Sky Sports analyst Thierry Henry says United should play Pogba further forward rather than sit back deep in midfield
Sky sources understand Manchester United will not pay Juventus' agent's fee.
Mourinho said the signing of Pogba was key to his plans to revitalise the club and believes the player can join the list of Old Trafford greats.
"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," he said.
Pogba: United return is destiny
Paul Pogba believes it was his "destiny" to return to Manchester United.
"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.
Pogba's plane arrives in Manchester before his medical ahead of a world record transfer to United
"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."
