Kvyat is currently second in the GP3 series, and has also competed in Euro F3 this year.
Team boss Franz Tost said: “He impressed our team with a strong performance and very informative technical feedback at the young driver test in Silverstone. This suggests that the basic qualities from which he can progress are all in place. Daniil can be sure that we will use all our experience of training youngsters to give him the best possible start to his Formula 1 career.”
Kvyat said: “Ever since I began karting, I wanted to get to Formula 1 and now that wish will become reality next season. I had a brief taste of working with the Toro Rosso team, when I drove for them at the Silverstone test and I enjoyed the experience very much. The fact I am based in Italy and speak Italian will, I am sure, help me to become part of the team very quickly.”