Epstein remarked towards the end of last season the future of the race was "not looking good" after the Texas state government announced a significant cut in its contribution towards COTA's hosting fee.
The state originally promised $25million per annum of funding over the 10 years of the contract with F1 supremo Bernie Ecclestone prior to the debut of the race in 2012.
That then dropped to around $19.5million after a different formula was applied to calculate the GP's economic impact on the area.
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Last year's race was also hit by a decline in ticket sales, while severe storms had a major impact on the event over the course of the three days, prompting fears it would fall off this year's calendar.
Up until recently the October 21-23 grand prixa was listed as provisional, but Epstein has now announced the race is on, and with a special programme of events to commemorate its fifth anniversary.
"We are so happy to confirm F1's return to COTA," said Epstein.
"Since we first hosted this event in 2012, we have gained a lot of knowledge and insight that has allowed us to make significant annual improvements to the event that we are confident will continue to establish the United States Grand Prix as the standout race weekend on F1's calendar.
"We're looking forward to welcoming visitors to Texas and the Circuit of The Americas, for what promises to be an amazing weekend."
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