The France international has now completed his world-record £89m deal, following a high-profile and long-drawn-out transfer saga.
Pogba left Old Trafford four years ago, having made just seven senior appearances under Sir Alex Ferguson.
The 23-year-old, who subsequently won four Serie A title with Juventus, has now clarified his reasoning for returning to Manchester.
“Leaving Manchester when I was 18 was a mutual decision between the club and me and the right thing to do at that moment,” he wrote. “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,” he added in another post.
“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.
“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.
“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 becomes the fourth signing of Jose Mourinho’s reign at Manchester United, following the Portuguese’s appointment in May.
Eric Bailly, Zlatan Ibrahimovic and Henrikh Mkhitaryan have also arrived through the door at Old Trafford this summer.