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Andy Friend's side were drawn in Pool 'B' with 11 other teams, but as a Tier 3 side will only face the Tier 2 teams home and away, meaning it's Racing and Bristol who will make trips to The Sportsground.
The other Pool B teams that Connacht will compete against for a spot in quarter-finals are Exeter Chiefs, Harlequins and Gloucester from the Premiership, Top 14 sides Lyon, Clermont and Toulouse, and fellow PRO14 teams Ulster, Munster and Glasgow.
Confirmed fixture details including dates and kick-off times will be announced in the coming days, however the games will take place on the weekends of 11th December, 18th December, 15th January and 22nd January.