Van Aanholt, 23, joins the Black Cats for an undisclosed fee and becomes their fourth new signing of the summer.
He has a pair of international caps to his name and was in former Netherlands boss Louis van Gaal’s 30-man provisional squad ahead of the recent World Cup, although he did not make it into the final 23-man party.
Van Aanholt joined Chelsea from PSV Eindhoven in 2007 but has made only eight appearances for the first team and has spent the last two seasons on loan with Vitesse Arnhem.
He now becomes the latest signing by Sunderland boss Gus Poyet, who has already brought in Billy Jones, Costel Pantilimon and Jordi Gomez this summer.
Poyet has been eager to add a new left-back, with Marcos Alonso's loan spell from Fiorentina having finished at the end of last season.