The 33-year-old Frenchman has penned a two-year deal with the Italian champions for a fee of around £950,000.
Evra leaves United following a successful eight-year spell at Old Trafford.
The full-back signed a new one-year contract with the Red Devils back in May before informing the club that he was keen to move on for personal reasons.
"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," he told United's official website.
Evra won five Premier League titles, three League Cups and the Champions League during his time with United.