The Netherlands international failed to break into the Chelsea first team with any regularity after signing in 2009, and was sent out for a number of loan spells at various clubs.
Included among those were Newcastle United, Leicester City and Wigan Athletic, while he 23-year-old spent the last two and a half years at Eredivisie outfit Vitesse.
Van Aanholt made 70 league appearances for Vitesse in that time, scoring five goals, and helped the club to sixth place in the Dutch top flight 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 becomes Sunderland's fourth signing of the close-season, after the arrivals of Billy Jones, Costel Pantilimon and Jordi Gomez.
