Ospreys will host Scarlets in Swansea in an all-Welsh European Challenge Cup tie on Sunday, 6 April (17:30 GMT).
Cardiff will travel to face top seeds Connacht in Galway on Saturday, 5 April (20:00 GMT), after the Irish province defeated Matt Sherratt’s side in the final group game.
Dragons failed to progress after finishing fifth in their pool.
The Ospreys and Scarlets Challenge Cup tie will be staged eight days after the two sides meet in the United Rugby Championship on Saturday, 29 March.
The European knockout match at Swansea.com Stadium is scheduled to take place a day after Ospreys’ football landlords Swansea City play a Championship match against Derby County on 5 April.
It will be a busy time for the ground with the Swans also due to host Plymouth on Wednesday, 9 April.
Swansea head coach Luke Williams expressed concern about the state of the Swansea.com pitch surface following their 2-1 defeat by Sheffield United.
