The Netherlands international sat out of Dynamo’s Ukrainian Super Cup defeat to Shakhtar Donestk on Tuesday night, and is poised to arrive on Wearside.
The 27-year-old, who began his career at AZ Alkmaar, scored eight goals for Dynamo last season and is likely to cost the Black Cats a fee in the region of £8m.
The versatile forward, who can play as either a winger or a striker, has made 29 appearances for his country – scoring eight goals.
Lens would be Sunderland boss Dick Advocaat’s fourth summer signing following the arrivals of Santiago Vergini, Sebastian Coates and Adam Matthews.
Sunderland continued their pre-season preparations in the United States with a 1-0 defeat to Sacramento Republic on Wednesday morning.
Advocaat’s side are next in action on Friday when they face Mexican club Pachuca.