The 23-year-old signed a four-year deal with the Black Cats for an undisclosed fee after passing a medical.
Altidore began his career at New York Red Bulls before heading to Spain with Villarreal, where he went on to enjoy loan spells at Xerez, Hull City and Bursaspor.
His one-year stay at KC Stadium saw him score once in 28 Premier League games, 12 as substitute, in the 2009/10 relegation season.
He moved from Villarreal to AZ in August 2011 and proved an instant hit, scoring 38 goals in 67 appearances.
The American has also registered 17 goals in 60 appearances for his country but will now join up with his new Sunderland team-mates at their pre-season training camp in Italy.
Having failed to score for the US since November 2011, he ended a lengthy goal drought in an international friendly victory over Germany in Washington DC last month.
He said: "'I'm thrilled to be here. It's a fantastic club, I'm really excited about this season and I'm excited to be a part of it."
Altidore joined goalkeeper Vito Mannone, defenders Valentin Roberge and Modibo Diakite, midfielder Cabral and winger David Moberg Karlsson as part of Paolo Di Canio's new-look squad at the Stadium of Light.