The French midfielder completed a move to the Italian giants on Monday, signing a four-year contract with the club.
His six-year stay at Old Trafford is officially at an end, with his departure coming under something of a dark cloud.
The 29-year-old proved to be a divisive figure in Manchester with fans frustrated at his inconsistent performances, despite knowing that he was capable of being one of the world's best players.
Pogba was asked about his decision to leave United during his unveiling, and said that he's confident that he can do better in the seasons to come.
He said: "I believe in destiny, I am happy with all the choices I've made. That's life.
"I am happy now. Who knows, had I won, choices could have been different."
He continued: "When you play for a team and change coach every season it's hard.
"It's true that I was injured sometimes. It was a bit of everything. Coach, team, change of roles, these things blocked me a little.
"Now, it's another Paul, another Pogba and hopefully, I won't have many injuries, I'll feel well and play in my role, doing better than in the last seasons."
Pogba returns for his second spell at Juve, having scored 34 goals and created an additional 40 in 177 appearances between 2012 and 2016.
Speaking about his decision to move to Juventus once again, Pogba said: "I spoke to Massimiliano Allegri also when I was at Man United, I spoke to him before coming here.
"He is here now, I spent many important years with him. This is the right moment with the right person.
"There were other clubs interested but when I chose Juventus, my heart told me that it was the right destination.
"When I saw Juventus fans sending me messages it was always nice, but I was focused on Man United.
"I've thought about coming back in the last year and I did it. I am happy for this and the fans too."