The Friday night fixture will take place at Kingspan Stadium at 19:35 BST.
It was confirmed earlier this week that the Cheetahs and Southern Kings would be joining the revamped competition.
The South African teams lost their place in the southern hemisphere Super Rugby, which is cutting from 18 teams to 15, at the end of last season.
The full list of fixtures for the first 13 rounds of the competition will be published on Monday, 7 August.
Ulster have been included in Conference B of the tournament and the Cheetahs in Conference A so the Belfast encounter will be their only meeting of the regular Pro14 season.
The landmark game will also represent the first competitive outing for new Ulster head coach Jono Gibbes and assistant coach Dwayne Peel, who have been recruited by the Irish province.
"This is a really exciting departure for the competition and we're delighted to be hosting the Cheetahs on the opening day, in what will be fantastic occasion under the lights of Kingspan Stadium," said Ulster Director of Rugby Les Kiss.
"South Africa is one of world rugby's great powerhouses with sides renowned for playing fast, open and uncompromising rugby so there is no doubt that both teams will add greatly to the Championship.
"The Cheetahs in particular are famous for their all-out attacking brand of rugby, and we also like to get the ball moving fast so I think it will make for a highly entertaining spectacle."
Ulster's opening match of the new Pro14 against South African side the Cheetahs will be shown exclusively live in the UK on BBC Sport NI on 1 September.