As reported by Motorsport.com, Kvyat had emerged as a surprise favourite to land a drive at the team that dropped him late last year.
This will be Kvyat’s third spell at Toro Rosso, the Russian having raced for the team in 2014 and then again from early-2016 after being demoted from the senior Red Bull team.
He was dropped from Red Bull after the 2017 United States Grand Prix and joined Ferrari as a development driver, but has been freed up to return to his original backer because Red Bull is promoting Pierre Gasly to replace Daniel Ricciardo.
Kvyat said: “First of all, I would like to thank Red Bull and Toro Rosso for giving me this opportunity to race in Formula 1 again and I am particularly pleased to be returning to a team I know very well.
“Toro Rosso has always made me feel at home and I’m sure it will still be the same next season.
“I would also like to thank Ferrari for trusting my driving skills which allowed me to stay connected to F1 as their development driver.
“Even if my duties were primarily simulator based, I’ve learnt a lot, and I now feel stronger and better prepared than when I left Toro Rosso.”
Kvyat said he “never gave up hope of racing again”, and Red Bull motorsport advisor Dr Helmut Marko told Motorsport.com recently that the Russian had matured in his brief time away.
Toro Rosso team boss Franz Tost said: “I believe he deserves another chance in Formula 1.
“Daniil is a high skilled driver with fantastic natural speed, which he has proven several times in his career.
“There were some difficult situations he had to face in the past, but I’m convinced that having had time to mature as a person away from the races will help him show his undeniable capabilities on track.
“We’ll push very hard to provide him with a good package, and I feel the best is yet to come from his side.
“That’s why we are happy to welcome him back to our team, to start a successful season together.”
Brendon Hartley claims to have a long-term deal but it is uncertain what Red Bull will do for the second seat.
Daniil Kvyat, Scuderia Toro Rosso STR12
Photo by: Alessio Morgese