Pogba arrived at United's Aon Training Complex in Chevrolet car provided by the club, having flown to the city from Nice.
He is due to undergo a medical and is expected to be officially confirmed as a United player on Tuesday or Wednesday.
British media reports say both club have agreed a world-record fee of 89 million pounds ($116.4 million, 105 million euros) to sign Pogba, not including agents' fees.
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United and Juventus confirmed on Sunday that Pogba has been granted permission to undergo a medical by the Turin club.
Manchester Airport had earlier tweeted a picture of a plane sitting on the runway, accompanied by the caption: "An important passenger has just touched down at the airport. Can anyone guess who it might be?"
Pogba, 23, left United in 2012 after making just seven appearances, but returns as one of the world's most famous players after winning four consecutive Serie A titles in Italy.
He will eclipse Gareth Bale as the world's most expensive player. The Welsh forward cost Real Madrid around 85 million pounds when he joined from Tottenham Hotspur in 2013.
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United manager Jose Mourinho hailed Pogba's arrival following his team's 2-1 win over Leicester City in Sunday's Community Shield at Wembley.
"I don't think Real Madrid were upset when they broke the record with Gareth Bale, with Cristiano (Ronaldo)," Mourinho said.
"When other people break records, I don't think it's a reason to be sad. I think it's a reason to be proud with the dimension of a club that can do that and can attract players of this dimension."
Pogba will become United's fourth close-season signing after Ivorian centre-back Eric Bailly, Armenian playmaker Henrikh Mkhitaryan and Swedish striker Zlatan Ibrahimovic.
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