Kvyat struggled to impress at Toro Rosso last season and was replaced by Pierre Gasly. He was previously dropped by sister team Red Bull in 2016
Red Bull reject Daniil Kvyat has been signed by Ferrari as their development driver.
The 23-year-old Russian's role will primarily involve work in the Italian team's simulator. There are no plans for Kvyat to test the car on track.