The 25-year-old has signed a four-year deal with the Mackems, and becomes the club's second signing on Friday following the acquisition of Steven Fletcher from Wolves.
Manager Martin O'Neill told the club's official website: “Adding quality players to the squad has been our main aim this summer and Adam certainly fits that bill.
“He has terrific ability, great delivery and I'm sure he is a player who will excite our fans. I couldn't be more delighted to have him at the football club.”
As exclusively revealed by Goal.com earlier this month, the Premier League champions had been set to sell Johnson after agreeing terms with Swansea City's Scott Sinclair, and the former-Middlesbrough man's departure has now paved the way for the 23-year-old's arrival.
Johnson's future at the club has been up in the air since the start of July, when the winger held talks over his future with boss Roberto Mancini, as also exclusively revealed by Goal.com, and his switch to the Stadium of Light brings an end to the saga.
|11/1||Sunderland are 11/1 to finish in the Premier League top six with Bet365|
However, he failed to maintain a first-team spot throughout his time at the Etihad Stadium, regularly featuring as a substitute during Roberto Mancini's tenure.
The north east-born wideman has 11 senior England caps but did not make Roy Hodgson's squad for Euro 2012 this summer.