The 33-year-old France international has signed a two-year contract with the Italian champions after ending his eight-and-a-half year stint at Old Trafford.
A Juventus statement read: "Juventus football club can today announce that Patrice Evra has signed a two-year contract with the club after a fee of £1.2million, to be paid in two separate instalments, was agreed with Manchester United.
"A further payment of £300,000 will be made to Manchester United in the event of Juventus qualifying for the 2015/16 Champions League."
Evra was closely linked with a move to Juve earlier this summer but ended up signing a one-year contract extension with United in May, with his previous deal poised to run out.
However, the experienced full-back, who would have been competing for a starting berth at United next season against big-money summer signing Luke Shaw, has now decided to move on anyway.
The popular former Monaco and Nice defender bids farewell to the Red Devils after nine hugely successful seasons that saw him make 379 appearances and help United win five Premier League titles, three League Cups, the Champions League and the Club World Cup.
He also deputised as United captain in the absence of Nemanja Vidic, who Evra could meet in Serie A next season after the Serbian moved to Inter Milan this summer.
Evra told ManUtd.com: "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.
"This club is steeped in history and I feel privileged to have become a part of that. I would like to thank everyone at the club – team-mates, coaches and in particular all the staff who made every single day in Carrington or at Old Trafford a special day.
"An immense thank you to Sir Alex Ferguson for making it all possible, for giving me the privilege to be a captain, to be inspired by the legend of Manchester United and to understand that nobody is bigger than the club.
"My biggest thanks go to the fans. We have had some fantastic times together, we lifted all of those trophies together and that night in Moscow will live with us all forever. Every single time I stepped out in that shirt I knew I was playing for the badge and 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."