The first leg is at Tannadice this evening, kick-off 7.45pm, with the return match at the Simple Digital Arena on Sunday at 3.00pm. Both ties will be shown live on BT Sport.
Dundee United won 2-1 when the teams met in Paisley in the Scottish Cup in February of this year while Saints' most recent success in this fixture was a 2-0 victory in the Ladbrokes Championship in December 2017.
Robbie Neilson's team finished second in the Championship this season and beat Inverness CT 4-0 on aggregate in the play-off semi-final. United have won five of their last six matches.
Oran Kearney's St Mirren are also in good form despite finishing 11th in the Premiership, above only relegated Dundee. Saints are unbeaten in their last six outings and have suffered just three defeats in 13 matches since mid-February.
There is no away goals rule in the play-offs so if the scores are level after two legs then extra time, and penalties if required, will determine the outcome.