The Austin race, where Lewis Hamilton clinched his third title in October, was thrown into doubt after the Texas state decreased its funding by more than €5m.
But the race, which takes place at the purpose-built Circuit of the Americas and is popular with both drivers and fans alike, will return for its fifth consecutive event later this year to ensure a record 21 grands prix in 2016.
“We had to make sure it was financially viable. That is largely what determines it and we have reason to have confidence the state is going to be a good partner.”
Regarding the circuit’s long-term future on the Formula One calender, Epstein added: “We are on very solid ground.”
Last year’s event was hit by unprecedented levels of rain which led to the cancellation of one practice session and saw qualifying delayed until Sunday. The circuit lost nearly $4m in refunds.
Ticket sales were also down on previous years with Epstein attributing the downturn in popularity to the nearby Mexican Grand Prix, which made its first appearance on the calender in more than two decades.
To that end, race organisers confirmed pop star Taylor Swift will perform after Saturday’s qualifying session.
Epstein added: “We had to make it financially irresistible to her, but it is our fifth-year celebration and we have reason to celebrate and sometimes you spend a little bit on special occasions.”
Meanwhile, American driver Alexander Rossi will return to Manor as their reserve driver for the upcoming campaign. Rossi will attend 11 races for the British-based team alongside his commitments to IndyCar.