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.
Kvyat, who was finally dropped by Red Bull in October after being demoted twice within 18 months, joins a large driver roster at Ferrari.
The team retained Sebastian Vettel and Kimi Raikkonen as race drivers in 2018.
Should either of them be unable to race, Ferrari have a number of options.
Prime among them would likely be Monegasque Charles Leclerc, a Ferrari protege who is to make his Formula 1 debut for Sauber this season.
Leclerc has been identified as the most likely successor to Raikkonen as Vettel's number two.
The veteran Finn is considered to be on his last chance at Ferrari after several lacklustre seasons and sources close to the team say Leclerc will replace him in 2019 as long as the 20-year-old Formula Two champion's development goes as expected this season.
Ferrari president Sergio Marchionne said at the team's Christmas lunch: "When things go right, it's a pleasure to see [Raikkonen] driving. In other moments it seems like he takes a break.
"He needs more consistency in terms of performance, but it's important to find the right key to make him driving like in Monaco also on other circuits.
"Probably this is the last season to find the right key and we must do it. I think it would be a shame if he left F1 without showing his real potential."
Marchionne added: "We see Leclerc, [Red Bull's Max] Verstappen and [Antonio] Giovinazzi, drivers with great skills, who can deliver a big change in the driver market. I'm still happy to have chosen Leclerc.
"I think that if we cannot find the right key for Raikkonen, the choice will fall on a young driver."
Italian Giovinazzi, 24, was Ferrari's reserve and third driver last season but this year has a similar role with Sauber, having been leapfrogged in the pecking order by Leclerc.
Sauber has effectively become a Ferrari satellite team this year and is carrying branding for the marque's sister company Alfa Romeo, which is to have high-profile involvement in F1 for the first time since 1985.
-- Courtesy of BBC Sport