However, the 19-year-old has claimed that he could have remained in English football had things have worked out differently.
"There was [interest] this summer with Chelsea and Arsenal, but it was less concrete," he told L'Equipe.
Despite opting to sign for a team that won the Serie A title last season, Pogba has set himself the target of forcing himself into the Juve starting lineup on a regular basis over the coming months.
"Impatient? Yes I am. When I want something, I'll do anything to get it. Today, I want to win a place in starting team of Juve and be one of the best players in the world," he added.
"I have not gone to Juve because I knew I was going to play in the starting team. I don't have any guarantees.
"The coach told me that there are a lot of games and he wanted a replacement for Pirlo and Vidal."
Pogba has been handed the number six shirt at the Juventus Stadium.