Evra signed a one-year extension to his contract in May but asked to leave when Juventus approached United over his availability.
The former Monaco defender would have been competing for a starting berth next season against £27m signing, Luke Shaw.
Evra, who featured for France as they got to the last 8 of the just concluded 2014 FIFA World Cup in Brazil, reflected happily on his time with United, where he made 379 appearances and scored 10 goals for the club since he joined in January 2006.
He said of his departure: “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.
“Joining and playing for Manchester United has been a privilege, a dream come true and my time here has been so memorable. Through the good times and the bad times we have all stuck together and remained loyal. I have always said you don’t just join Manchester United, you join the family and long may that tradition continue.
“This club is steeped in history and I feel privileged to have become a part of that. Over the past nine years I have met and worked with some incredible people, many of whom will remain friends for life. I would like to thank everyone at the club – teammates, coaches and in particular all the staff who made every single day in Carrington or at Old Trafford a special day.
He also thanked former manager, Sir Alex Ferguson and the club’s fans.
“An immense thank you to Sir Alex for making it all possible, for giving me the privilege to be a captain and to understand that nobody is bigger than the club”, he said.
“My biggest thanks go to the fans. We have had some fantastic times together and every single time I stepped out in that shirt I knew I was playing for a very special club.
“My passion for this club will live on and I know you guys will go on to enjoy more success in the coming seasons.”
It is understood that the Serie A Champion would pay an initial £1.2m for Evra, plus an extra £300,000 if they qualify for the Champions League in 2015-16.
Evra won five Premier League titles, three League Cup triumphs as well as an UEFA Champions League and FIFA Club World Cup winner’s medal.