The France international enjoyed a successful first stint at the club between 2012 and 2016, winning Serie A four times in a row and and the Coppa Italia twice.
"I am back, I am here and I can't wait to get started," Pogba told the club's Twitter account."I am very, very happy. "I can't wait to get started and wear this Juventus jersey again."
Sources told ESPN last month that Pogba agreed a move back to Juventus and he has now signed a four-year contract to reunite with manager Massimiliano Allegri.
At the start of June, United confirmed that he would leave when his contract expired, bringing an end to a difficult spell at Old Trafford. Pogba returned to United in 2016 for a then-world-record fee of £89.3 million from Juventus and won three trophies in his debut campaign. However, he fell out with then-United manager Jose Mourinho and struggled to find consistency under Ole Gunnar Solskjaer and interim boss Ralf Rangnick.
Pogba endured an easy relationship with the United fans and they booed him in his final two appearances against Norwich City and Liverpool. He will be hopeful of helping Juventus regain the Serie A title for the first time since 2020.
Pogba becomes the latest high-profile player to join the Bianconeri after Angel Di Maria signed for Juventus on Friday.