The 31-year-old England international has signed up with the Black Cats on a deal until June 2015.
Sunderland had a joint bid of more than £12million for Brown, John O'Shea and Darron Gibson accepted last month, and Republic of Ireland defender O'Shea was also on Wearside on Thursday for a medical.
Black Cats manager Steve Bruce said: "We are delighted to welcome a player of Wes' ability, experience and character to the club.
"He has been a fantastic professional for Manchester United through the years and not only will he strengthen our defensive options, he will also bring with him a winning mentality and level of maturity which can only be positive for the players around him."
Brown is Bruce's seventh summer signing after Ahmed Elmohamady, Connor Wickham, Craig Gardner, Ji Dong-won, Keiren Westwood and Sebastian Larsson, and is unlikely to be the last with O'Shea and Blackpool midfielder David Vaughan also understood to be close to agreeing deals.
The defender made senior 361 appearances for United over 15 years as a professional having joining the club as a 12-year-old, and has five Premier League winners' medals.
Brown won 23 England caps before announcing his retirement from the international game last summer.
He will bring a welcome versatility and vast experience to the Stadium of Light, where his arrival will go some of the way to making up for the loss of loan signings Nedum Onuoha and John Mensah.
Ostensibly a central defender, he can also play at right-back and with O'Shea equally comfortable across the back four as well as in midfield, Bruce could have healthy options at the back next season.
United boss Sir Alex Ferguson admitted it had been a tough decision to allow Brown to leave the club.
He told United's website: "Wes has been a great asset to the club during the most successful period in its history.
"He was a product of the youth system and marked himself out from an early age as one of his generation's most natural defenders.
"In his time with us, he certainly became a favourite with the fans for his no-nonsense approach to the game and his infectious personality.
"It's always the hardest of decisions to let loyal servants go. But life moves on and, unquestionably, Wes will get the chance to make a real contribution to Steve Bruce's Sunderland, and I'm delighted to be passing him into such good hands.
"Everyone connected with United wishes him a long and happy stay at Sunderland."
Meanwhile, Sunderland have appointed Bryan 'Pop' Robson as their new chief scout.
The Sunderland-born former striker, who returns to Wearside from his last post as an international scout for Chelsea, played 174 times for the club during three spells, served as reserve-team coach and Academy director and even stood in as caretaker manager.
He said: "Sunderland is obviously a club very close to my heart. I had great times here both as a player and as a coach, so I'm thrilled to be back working with Steve Bruce and his excellent management team."