Pogba helped France win the 2018 World Cup in Russia
It is understood the 29-year-old France midfielder will have a medical at the weekend before completing the move.
Pogba joined United from the Italian side in 2016 for a then world-record fee of £89m.
United and Pogba failed to agree on a new contract and the club confirmed at the start of June that he would leave as a free agent this summer.
It is anticipated Pogba will begin training with Juventus next week prior to their trip to the United States, where they will face Barcelona and Real Madrid on 27 and 30 July respectively.
For the second straight season, Juventus finished fourth in Serie A, 16 points behind champions AC Milan.
They had been Italian champions for the preceding nine seasons, with Pogba playing a key role in their title wins from 2012-13 to 2015-16.
He scored 34 goals from 178 games in his previous spell with Juventus having also joined on a free from United in 2012, after coming through the Old Trafford academy.
During his first season back at Old Trafford, Pogba helped United win the EFL Cup and Europa League but they would prove to be the only trophies he won in his second spell.
A disagreement with then manager Jose Mourinho saw him lose the vice-captaincy in 2018 and injuries and sporadic form reduced his impact.
Pogba, who joined the United academy from Le Havre as a 16-year-old in 2009, was influential as France won the World Cup in Russia in 2018 and scored 16 goals for United in 2018-19.
But over the last three seasons he scored eight goals from 91 appearances, with one from 27 last term.
"It was a low-key end to a United career that brought so many individual high moments," read a United statement earlier this month when they announced Pogba was to leave.
United offered him an extension and BBC Sport understands it was a more lucrative offer than his previous deal but in an Amazon Prime documentary 'The Pogumentary', he said the club was "bluffing".
Pogba scored 39 goals in 233 appearances across his two spells at the club but his final home appearance against Norwich City in April saw him jeered by his own supporters as he was substituted.
He expressed gratitude for the "unconditional support from the fans" in a message on social media following the club's announcement that he was leaving.
-- Courtesy of BBC Sport