The 33-year-old extended his long stay at Old Trafford with a new one-year deal in May, but has now performed a U-turn over his future and opted to head to Italy.
Evra has penned a two-year contract with Massimiliano Allegri's men and joins former United team-mates Carlos Tevez and Paul Pogba in Turin.
Juve have paid a fee of £1.6 million for the France international's services, which will be paid in two instalments of £0.6m.
A further £0.3m will be payable should Juve qualify for the 2015-16 UEFA Champions League.
In a statement released via United's official website, Evra said: "After a great deal of thought I have decided the time is right for me to leave Manchester United.
"It is the biggest decision of my career as this club is, and will always remain, in my heart."
Evra made 379 appearances for United after joining from Monaco in January 2006.
He won five Premier League titles, the Champions League, the Club World Cup and three League Cups in a trophy-laden spell at Old Trafford.
