Red Bull-owned Toro Rosso act as a feeder team to former champions Red Bull Racing, both of whose drivers Max Verstappen and Pierre Gasly graduated from Tost's outfit.
Both teams will have Honda engines after Red Bull Racing ended their partnership with Renault at the end of 2018, with Toro Rosso using some non-listed parts designed for last year's race-winning Red Bull.
Toro Rosso's new lineup will be experienced Russian Daniil Kvyat, who was both promoted and dropped by the team before securing a comeback seat, and British-born Thai newcomer Alexander Albon.
Albon, who raced in Formula Two last year, said he would be taking the season step by step and not setting any long-term goals either.
"If you start setting long-term goals, you just put unnecessary pressure on yourself. I’m just focused on myself and let’s see how it all goes," he said.
The blue, silver and red car, whose unveiling came after Haas F1's livery launch last week, reflected new aerodynamic restrictions with a simpler front wing and barge-board arrangement.