The 23-year-old left-back, who has spent the last two and a half seasons at Vitesse Arnhem, has signed a four-year deal with the Black Cats.
He played eight times for Chelsea and also had loan spells at Wigan, Leicester, Newcastle and Coventry.
He has two caps for the Netherlands but missed out on the World Cup after being named in the 30-man provisional squad.
Sunderland head coach Gus Poyet was keen to sign a left-back after Marcos Alonso's loan spell finished at the end of last term.
Fiorentina defender Alonso made 20 appearances for the Wearsiders in 2013-14 but has been part of the Viola's pre-season campaign this summer.
Poyet has already signed defender Billy Jones from West Brom, Wigan midfielder Jordi Gomez and goalkeeper Costel Pantilimon from Manchester City so far this transfer window.
Fabio Borini has also been linked with a return to Wearside, with a fee agreed with Liverpool, although Poyet has admitted his frustration at delays in adding new players this summer.
Sunderland have signed Netherlands international Patrick van Aanholt from Chelsea for an undisclosed fee.