This is an almost identical pool for the westerners to their one in the 2005/06 tournament, when they had Worcester, Montpellier and Catania as their opponents.
Back then, Connacht beat Montpellier home and away and lost 30-20 to Worcester at Sixways Stadium before winning the return leg 22-21 at the Sportsground.
Connacht were drawn in the same pool as French outfit Montpellier the following season (2006/07), winning at home (26-13) but losing away (35-22).
Indeed, Connacht also met Montpellier in the second round of the 2004/05 competition, progressing to the quarter-final stage with an aggregate win of 70-22.
Olympus Rugby XV Madrid are a Spanish invitation team and will play their home matches at Estadio Universidad Complutense.
Monday's European Challenge Cup draw, made in the ERC offices in Dublin and scrutinised by the IRB's Head of Legal Affairs Susan Ahern, saw former Heineken Cup and European Challenge Cup champions draw Rugby Calvisano, Bayonne and tournament newcomers Racing-Metro 92 in Pool 4.
Bourgoin, the 1997 winners and last season's beaten finalists, will be up against Leeds Carnegie, Overmach Rugby Parma and Bucuresti Oaks in Pool 1.
The five tier 1 teams - London Wasps, Saracens, Bourgoin, Newcastle Falcons and Worcester Warriors - were kept apart in separate pools.
Only French clubs were drawn in the same pools as they will have eight teams taking part in the competition.
Connacht reached the quarter-finals of the 2008/09 European Challenge Cup, losing 42-13 to eventual champions Northampton Saints. It was the first time the province had reached the last-eight since 2006.
2009/10 EUROPEAN CHALLENGE CUP POOLS:
POOL 1: Bourgoin, Leeds Carnegie, Overmach Rugby Parma, Bucuresti Oaks
POOL 2: Worcester Warriors, CONNACHT, Montpellier, Olympus Rugby XV Madrid
POOL 3: Saracens, Castres Olympique, Toulon, Rugby Rovigo
POOL 4: London Wasps, Rugby Calvisano, Bayonne, Racing-Metro 92
POOL 5: Newcastle Falcons, Montauban, Petrarca Rugby, Albi
2009/10 EUROPEAN CHALLENGE CUP TIERS -
TIER 1: London Wasps, Saracens, Bourgoin, Worcester Warriors, Newcastle Falcons
TIER 2: Castres Olympique, Leeds Carnegie, Rugby Calvisano, CONNACHT, Montauban
TIER 3: Montpellier, Overmach Rugby Parma, Bayonne, Petrarca Rugby, Toulon
TIER 4: Rugby Rovigo, Racing-Metro 92, Albi, Bucuresti Oaks, Olympus Rugby XV Madrid
2009/10 EUROPEAN CHALLENGE CUP FIXTURES -
ROUND 1 - October 8-11, 2009
ROUND 2 - October 15-18, 2009
ROUND 3 - December 10-13, 2009
ROUND 4 - December 17-20, 2009
ROUND 5 - January 14-17, 2010
ROUND 6 - January 21-24, 2010
QUARTER-FINALS - April 8-11, 2010
SEMI-FINALS - April 30-May 2, 2010
EUROPEAN CHALLENGE CUP FINAL - May 21/22/23, 2010