The 23-year-old becomes Gus Poyet's fourth summer signing, joining Billy Jones, Costel Pantilimon and Jordi Gomez at the Stadium of Light.
Van Aanholt made 70 league appearances for Vitesse in a two-year loan spell, scoring five goals, and helped the club to sixth place in the Eredivisie last season.
He made just four league appearances for Chelsea in his five years at Stamford Bridge, all as a substitute, and the defender will be looking to experience regular Premier League action at Sunderland.
"We would like to thank Patrick for his service and wish him the best of luck for the future," read a statement on Chelsea's official website.
Van Aanholt, who has two international caps, was called up to Louis van Gaal's provisional Netherlands squad of 30 prior to the World Cup but did not make the cut as the Oranje went on to claim third place in Brazil.
The left-sided defender also spent time at Sunderland's rivals Newcastle during a loan spell in 2010 - one of five clubs he has spent time on loan with.