The 19-year-old, who will race alongside Jean-Eric Vergne at the Toro Rosso team from next year, drove a two-year-old STR6 at the Misano circuit last Friday to complete the required mileage to be granted the licence.
Kvyat managed 102 laps, equivalent to around 402 kilometres.
The requirement for a Superlicence is 300kms plus an outstanding single-seater record.
"It was important to do 300 km, so we did it," he said.
"I event didn't know what car it was, of course it was not STR8 I drove at Silverstone this summer, but something quite similar to it.
"With stable technical regulations machinery teams' machinery has mostly been the same for last two or three years. Of course, I expect much more changes next season."
Kvyat, who had previously just completed 22 laps in an F1 car, secured this year's GP3 championship in Abu Dhabi earlier this month.
The Russian will replace Vergne for practice one in the US and team-mate Daniel Ricciardo on Friday morning in Brazil.
Kvyat said he did not yet know what his exact programme for US GP practice would involve.
"I think the team will finalise our programme on Thursday," he said. "With tests in modern cars strictly restricted, every lap counts.
"So my target is to drive as much as possible, at the same time providing my engineers with information and learning the circuit for next year."