Scarlets will take on Ospreys next month for a place in next season’s European Champions Cup.
Glasgow’s comprehensive 34-10 win over Edinburgh in Scotstoun means the Scarlets finished fourth in the Guinness PRO14 Conference B standings after the regular season.
The play-off will be hosted by the Ospreys, who finished with more league points than the Scarlets after 21 rounds.
The PRO14 have confirmed that a provisional date for the match has been identified and will be confirmed in due course.
PRO14 Rugby will also need to take account of whether an additional eighth Champions Cup place might be available were Leinster to win the European tournament and all four Challenge Cup semi-finalists have already qualified through their domestic leagues.
Scarlets were beaten 34-32 by the Dragons in the Judgement Day finale at the Principality Stadium, leaving them with an anxious wait for the result of the Glasgow-Edinburgh clash.
But Glasgow's victory means Wayne Pivac’s side will lock horns with their arch rivals in a game that will decide who will carry the flag for Wales in the top tier of European competition next season.
Reflecting on the game, Pivac said: “If you look at the first quarters of both halves, we gave away points and didn’t really start how we would have liked to. The urgency and aggression wasn’t there.
“We talked about it at half-time and expected a better start to the half, but we didn’t get it and of course the intercept try got them back into it and put more pressure on us.
“The Dragons have always been a tough opponent for us every year here. We did what we usually do against them, getting a bonus-point try, but it was the points conceded that was the issue.
“You have to take the good with the bad. We’ve had some real highs in the last couple of seasons, but this one has been frustrating. Today’s performance probably typified our season, some great play and some poor play.
“Obviously, the result wasn’t what we wanted, but in terms of qualifying for next year’s Champions Cup we are still alive.”