Challenge Cup holders Cardiff Blues will travel to face Lyon in their first Heineken Champions Cup match for four years on Sunday, 14 October.
Last season's semi-finalists Scarlets welcome French side Racing 92 on Saturday, 13 October.
The Ospreys and Dragons are in Challenge Cup action the same day as the Scarlets.
Ospreys welcome Pau while the Dragons travel to Romania to play Timisoara Saracens.
The draw was initially made in June with the Scarlets pitted against Racing 92, Leicester and Ulster in Pool 4.
Blues won last season's Challenge Cup but return to the top tier competition and play Saracens, Glasgow and Lyon in Pool 3.
Ospreys are in European club rugby's second tier and face Pau, Worcester and Stade Francais in Pool 2.
Dragons were drawn in Pool 1 against Northampton, Clermont Auvergne and Romanian side Timisoara Saracens.
Scarlets reached the semi-finals of the Champions Cup last season before losing 38-16 to Leinster and face Irish opposition again in the shape of Ulster, plus English side Leicester and Racing of France.
Ospreys lost their Pro14 play-off with Ulster to qualify for the Champions Cup, but will still face a tough task in the Challenge Cup against two French teams - Pau and Stade - plus English side Worcester, who have Wales wing Josh Adams in their squad.
Three-time Champions Cup finalists Clermont of France and English side Northampton, the 2000 European champions, will provide stiff competition for Dragons, while Romanians Timisoara provide less familiar opposition.
The first round of European games will take place on 12/13/14 October, with the final pool fixtures on 18/19/20 January 2019.
The quarter-finals are set for 29/30/31 March 2019, with the semi-finals scheduled on 19/20/21 April 2019.
The Champions Cup final will be played at St James' Park, Newcastle, on 11 May 2019, with the Challenge Cup final the day before at the same venue.
Champions Cup 2018-19 draw:
Pool 1: Leinster, Wasps, Toulouse, Bath
Pool 2: Castres, Exeter Chiefs, Munster, Gloucester
Pool 3: Saracens, Glasgow Warriors, Lyon, Cardiff Blues
Pool 4: Scarlets, Racing 92, Leicester Tigers, Ulster
Pool 5: Montpellier, Newcastle Falcons, Edinburgh, Toulon
Challenge Cup 2018-19 draw:
Pool 1: Northampton, Clermont Auvergne, Dragons, Timisoara Saracens
Pool 2: Pau, Ospreys, Worcester, Stade Francais
Pool 3: Sale Sharks, Connacht, Bordeaux-Begles, Perpignan
Pool 4: La Rochelle, Zebre, Bristol, Enisei-STM
Pool 5: Benetton, Harlequins, Agen, Grenoble.
Sunday, 14 October, Lyon v Cardiff Blues, Matmut Stadium de Gerland, 14:00
Sunday, 21 October, Cardiff Blues v Glasgow, Arms Park, 15:15
Sunday, 9 December, Saracens v Cardiff Blues, Allianz Stadum, 13:00
Saturday, 15 December, Cardiff Blues v Saracens, Arms Park, 13:00
Sunday, 13 January, Glasgow v Cardiff Blues, Scotstoun, 15:15
Saturday, 19 January, Cardiff Blues v Lyon, Arms Park, 13:00
Saturday, 13 October, Scarlets v Racing 92, Parc y Scarlets, 17:30
Friday, 19 October, Leicester v Scarlets, Welford Road, 19:45
Friday, 7 December, Scarlets v Ulster, Parc y Scarlets, 19:45
Friday, 14 December, Ulster v Scarlets, Kingspan Stadium, 19:45
Saturday, 12 January, Scarlets v Leicester, Parc y Scarlets, 17:30
Saturday, 19 January, Racing 92 v Scarlets, Paris La Defense Arena, 15:15
Saturday, 13 October, Ospreys v Pau, Liberty Stadium, 15:00
Saturday, 20 October, Worcester v Ospreys, Sixways, 15:00
Saturday, 8 December, Ospreys v Stade Francais, Liberty Stadium, 15:00
Friday, 14 December, Stade Francais v Ospreys, Stade Jean Bouin, 19:45
Saturday, 12 January, Ospreys v Worcester, Liberty Stadium, 15:00
Friday, 18 January, Pau v Ospreys, Stade du Hameau, TBC
Saturday, 13 October, Timisoara v Dragons, Dan Paltinisanu Stadium, 14:30
Friday, 19 October, Dragons v Northampton, Rodney Parade, 19:30
Saturday, 8 December, Northampton v Dragons, Franklin's Gardens, 15:00
Saturday, 15 December, Clermont Auvergne v Dragons, Stade Marcel Michelin, 14:00
Friday, 11 January, Dragons v Timisoara, Rodney Parade, 19:30
Friday, 18 January, Dragons v Clermont Auvergne, Rodney Parade, 19:45.