OFFICIAL: Paul Pogba Rejoins Juventus FC After Five Years
He flew in to Turin on Friday for his medical before the announcement on Monday.
Pogba had not featured for United since April after struggling with injury and sporadic form.
Juventus said: “When we say goodbye after an intense adventure shared together, there is always a glimmer of hope that we will see each other again, sooner or later.
Pogba, who joined the United academy from Le Havre as a 16-year-old in 2009, helped them to win the EFL Cup and Europa League in his first season back at the club, but they would prove to be the only trophies he won in his second spell.
Pogba, who has 91 international caps, was influential as France won the World Cup in Russia in 2018.
Juventus finished fourth in Serie A for the second straight season, 16 points behind champions AC Milan.