The STR12, which had already made its track debut in a run at Misano last week, features a completely new look compared to its previous model.
Instead of the traditional paint scheme seen over the past couple of seasons, the STR12 sports a striking blue and red livery, the colours used for Red Bull’s Simply Cola beverage.
Apart from a new look, Toro Rosso will also use a new power unit this year, the Faenza-based squad returning to Renault engine after running year-old Ferrari engines in 2016.
The STR12, designed by a technical team led by James Key, incorporates the shark fin seen in most new cars so far this year.
As for Kvyat, he rejoined the team after losing his Red Bull seat to Max Verstappen from the Spanish Grand Prix onwards, and secured a contract extension for 2017.
Toro Rosso will join all its rivals at Barcelona from next week, when official pre-season testing will kick off.