The 33-year-old left-back has signed for the Bianconeri on a two-year deal for an undisclosed fee thought to be in the region of £1.5millon.
Evra, a France international who has played over 300 times for United, was given permission to leave Old Trafford following the signing of England international Luke Shaw from Southampton.
Evra had signed a one-year contract extension in May, but the defender was one of only a handful of names that did not travel with the squad on their pre-season tour of the USA last week.
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. 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.
"I feel the move to Juventus, at this stage in my career, is the right one in order that I can continue to challenge myself. Juventus is a great club and I am looking forward to helping them continue the fantastic success they have enjoyed in their prestigious history."
Born in Senegal, Evra grew up in France but began his professional career in Sicily with Marsala before moving to Monza and then French Ligue 1 club Nice in 2000.
He then spent four-years playing for neighbouring Monaco and played over 100 times before he was signed by Sir Alex Ferguson at Manchester United in 2006.
Evra enjoyed an illustrious eight-year career at Old Trafford, winning the Champions League in 2008, five Premier League titles, three League Cups and a Club World Cup.
He made a total of 379 appearances for United, scoring 10 goals, and he has 57 caps for France.