The 33-year-old, who signed a new one-year contract with United in May, has committed to a two-year deal with the Serie A champions.
Evra's departure leaves �30 million signing Luke Shaw as the only specialist left-back in United's first-team squad, after Alexander Buttner moved to Dynamo Moscow.
On the announcement of the move, Evra told United's official website: "After a great deal of thought I have decided the time is right for me to leave Manchester United.
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