Red Bull also announced on Tuesday that Alexander Albon would remain at the team for next year, eliminating both Toro Rosso drivers from contention for the seat.
However, both will stay in F1 next year and partner each other for a full season.
Kvyat originally joined Toro Rosso in 2014, speaning one year at the team before moving to Red Bull for the 2015 campaign. However, after a handful of rounds into the 2016 season, he was demoted back to Red Bull.
Towards the end of the 2017 season, Kvyat was dropped completely from the Red Bull programme, only to be brought back in 2019 after spending a year working with Ferrari.
“It’s great to be confirmed with the team for 2020," Kvyat said. "I’m really happy because I feel very comfortable with everyone here, I know the team and they know me very well, so it’s easy to understand everyone’s needs.
"We’ve achieved great things together, like our podium this year in Germany, so I hope to deliver a very strong season again for this team next year.
"I’m grateful for the opportunity to continue in Formula 1 and I will give it my all to show the best possible performances next year. I’m really looking forward to more exciting times together.”