Guinness PRO12 rivals Munster and Glasgow Warriors will meet in Pool 1 following the draw for the Champions Cup and Challenge Cup.
They will be joined by three-time European Champions Leicester Tigers and last year's runners-up Racing 92 while in Pool 3 Scarlets face trips to reigning champions Saracens, Toulon and Sale Sharks.
Guinness PRO12 runners-up Leinster face Montpellier, Northampton Saints and Castres in Pool 4 with Ulster facing two French sides in Clermont and Bordeaux-Begles as well as English runners-up Exeter Chiefs in Pool 5.
Martin Anayi, managing director of PRO12 Rugby, said: "I am really looking forward to seeing all twelve Guinness PRO12 clubs in European action this season.
"There are a number of mouth-watering ties that I am sure fans will be extremely excited about including Scarlets taking on the past two European Champions in Saracens and Toulon.
"The European Champions Cup and the European Challenge Cup are always great competitions and I expect to see the Guinness PRO12 clubs once again making an outstanding contribution to them."
Ieuan Evans, who conducted the draw with Dmitri Yachvili, said: "I am really looking forward to (Champions Cup) Pool 5, there's sides there that like to play expansive attractive rugby so that's one to watch.
"And I am interested to see how Connacht go, they played some breath-taking rugby in the Guinness PRO12 final."
In the Challenge Cup, top seeds Ospreys were drawn against last year's semi-finallists Grenoble, Newcastle Falcons and Lyon.
While Cardiff Blues face two close neighbours in Pool 4 after they were drawn against Bath and Bristol Rugby as well as a trip to France to take on Pau.
Edinburgh Rugby are in Pool 5 with last year's runners-up Harlequins, Stade Francais and Romanian club Timisoara Saracens.
Newport Gwent Dragons meet Brive, Worcester Warriors and Russian club Enisei STM while Benetton Treviso will play La Rochelle, Gloucester Rugby and Bayonne.
The first round of fixtures will take place on the weekend of October 13/14/15/16 followed by round two a week later.
Round three will take place on 8/9/10/11 December, with round four the following week before the final group games in January 2017.
Both the Challenge Cup and the Champions Cup finals will be played at BT Murrayfield Stadium on Friday 12 May, 2017 and Saturday 13 May, 2017 respectively.
Full Draw:
European Rugby Champions Cup:
Pool 1 - Racing 92, Glasgow Warriors, Leicester Tigers, Munster
Pool 2 - Connacht, Wasps, Toulouse, Zebre
Pool 3 - Saracens, Toulon, Scarlets, Sale Sharks,
Pool 4 - Leinster, Montpellier, Northampton Saints, Castres
Pool 5 - Exeter Chiefs, Clermont, Ulster, Bordeaux
European Rugby Challenge Cup:
Pool 1 - La Rochelle, Gloucester, Treviso, Bayonne
Pool 2 - Ospreys, Grenoble, Newcastle Falcons, Lyon
Pool 3 - Brive, Worcester, Newport Gwent Dragons, Enisei STM
Pool 4 - Cardiff Blues, Bath, Pau, Bristol
Pool 5 - Harlequins, Edinburgh, Stade Francais, Timisoara Saracens
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