The Guinness Pro14 offshoot will kick off later in April with the four South African teams scheduled to compete against each other during the opening three rounds.
Edinburgh kick off their campaign at home to Zebre on Friday April 23 with Glasgow facing Benetton in Treviso the following day.
The inter-city rivals then meet in evening derby matches at Scotstoun on Friday May 7 (8.15pm kick-off) and at BT Murrayfield on Saturday May 15 (7.35pm kick-off).
Doubt was cast on the involvement of the South African teams this week due to coronavirus, with reports suggesting they would not be granted visas to come to the UK because of concerns about the South African variant of Covid-19.
The Bulls, Lions, Sharks and Stormers are due to play away games in Europe in rounds four to six of the competition but the fixtures remain unconfirmed.
A Pro14 statement said: “Confirmation for Rounds 4-6 will follow once PRO14 Rugby has received all necessary approvals and permissions from the relevant governments and health authorities for the South African teams to travel.”
The tournament is due to finish with a final on June 19 following the six rounds of fixtures.
The Rainbow Cup begins the assimilation of the South African sides into the European game, with the four franchises expected to join an expanded Pro14 set-up.
Premier Sports will broadcast Rainbow Cup matches in the UK.