The 23-year-old completed his switch back to United from Italian champions Juventus in the early hours of Tuesday morning after ongoing speculation surrounding his future, reports Sky Sports.
Pogba, who won four Serie A titles during his time in Turin, completed his medical on Monday before signing a five-year deal.
"Thanks @juventusfc and all Juventini. Goodbye means nothing, it is the time we spent together that matters," Pogba tweeted on Monday.
The French midfielder left United for Turin back in 2012 having made just seven substitute appearances under then United coach Alex Ferguson.
In a series of Instagram posts, he admitted he was frustrated how long it took the world-record transfer to be completed.
"This transfer took so long because it was a huge decision and involved lots of thinking and work. The wait was as annoying to me as it was to you," Pogba said.
"To all supporters who wrote on my pages about transfer rumours, I have read you all and thank you for the passionate messages. My apologies for not responding before, by law I could not talk."
Pogba is likely to make his debut in Manchester United's opening English Premier League game against Bournemouth on August 14.
"Leaving Manchester when I was 18 was a mutual decision between the club and me and the right thing to do at that moment. Now it's time to go back and forward, Old Trafford here I come! My deepest respect to the clubs who considered having me. Gracias, merci!" the 23-year-old said.
"Juventus will always be a part of me and I will always miss, love and be grateful to the club, the team and especially the supporters. I hope you can respect my decision. The most beautiful part of friendship is to understand and be understood. It is difficult to explain so much in a few lines but I made a decision guided by my heart and nothing else," the French international added.
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