Moscow-based online newspaper Lenta reports that, mere days after Red Bull decided to demote 22-year-old Kvyat, Russian businessman Sergey Belousov signed on the dotted line of a sponsorship deal with the Faenza-based team.
"We have been familiar with Daniil Kvyat for a long time and discussed a possible partnership with Toro Rosso before his move to Red Bull," Belousov, an IT entrepreneur and venture capitalist, said.
"We also have a huge respect for the head of Toro Rosso, Franz Tost."
Belousov's financial and technological support for Toro Rosso will apparently be long-term, but only if Tost and Kvyat are at the team.
He said that he thinks Toro Rosso is a better place for Kvyat than Red Bull Racing.
"Red Bull is focused on the commercial side as well but Toro Rosso is pure racing," said Belousov.
"I am not an expert in Formula 1, but in my opinion Toro Rosso is more comfortable at Toro Rosso.
"Of course, [Max] Verstappen is also a first-class driver, but I think Kvyat was able to show his strength already at the start of this season."
The Spanish Grand Prix takes place next Sunday.