Current cup holders Leinster 'A', who secured victory over English Championship winners Newcastle Falcons in a thrilling final at Kingston Park, begin their title defence against newcomers Ealing Trailfinders.
The west London club will make their debut in the competition, having been promoted from SSE National League 1 to the second tier in May.
Bristol, the 2011 British & Irish Cup winners, will kick off their cup campaign by welcoming fellow Championship club Leeds Carnegie to the Memorial Stadium, while inaugural winners of the trophy, Cornish Pirates, will host Ulster Ravens in Penzance.
Munster 'A', who are the top seeds in Pool 4, will also start their British & Irish Cup with a home game, hosting Stirling County from the Scottish Premier Division.
Connacht Eagles, who have been placed in Pool 3 alongside Bedford Blues and Rotherham Titans, will be away to Welsh opposition in the opening round.
Commenting on the 2013/14 British & Irish Cup, RFU professional rugby director Rob Andrew said: "The British & Irish Cup offers up some really traditional clashes between old rivals, and this season promises to be no different.
"With the revision to the structure and a reduction in clubs, the organising committee is confident that this will be one of the most competitive seasons yet in the competition."
As revealed in April, the British & Irish Cup has been revised for the 2013/14 season, moving from 32 teams to 24, playing in six pools of four.
Four Welsh Premiership teams will now represent Wales in the competition, joining the 12 clubs from the English Championship as well as four from each of Ireland and Scotland.
The selection of the Welsh teams will be based on regional play-offs at the start of next season, with final positions in this season's Principality Premiership giving teams home advantage.
2013/14 BRITISH & IRISH CUP STRUCTURE:
* 12 English Championship clubs
* 4 Welsh Premiership clubs
* 4 Irish provinces - Connacht Eagles, Munster 'A', Leinster 'A' and Ulster Ravens
* 4 Scottish teams - top 4 finishers in the Scottish Premier Division: Ayr, Gala, Stirling County and Edinburgh Academicals
Pool stages -
* 6 pools of 4 playing home and away
* 4 points for a win, 2 for a draw, 1 bonus point for a) scoring 4 or more tries and/or b) losing by 7 points or less
* Top side in each pool progresses to knockout stages, plus two best runners-up
* 8 quarter-finalists ranked with teams ranked 1-4 having home advantage
Semi-finals and final -
* Four winning quarter-finalists progress to semi-final draw
* Winning semi-finalists progress to final
POOL 1: LEINSTER 'A', Wales 3, Moseley, Ealing Trailfinders
POOL 2: London Welsh, Wales 2, London Scottish, Edinburgh Academicals
POOL 3: Bedford Blues, Rotherham Titans, Wales 4, CONNACHT EAGLES
POOL 4: MUNSTER 'A', Nottingham, Plymouth Albion, Stirling County
POOL 5: Bristol, Wales 1, Leeds Carnegie, Gala
POOL 6: Cornish Pirates, ULSTER RAVENS, Ayr, Jersey
Round 1 -
Pool 1: Leinster 'A' v Ealing Trailfinders, Wales 3 v Moseley
Pool 2: London Welsh v London Scottish, Edinburgh Academicals v Wales 2
Pool 3: Rotherham Titans v Bedford Blues, Wales 4 v Connacht Eagles
Pool 4: Plymouth Albion v Nottingham, Munster 'A' v Stirling County
Pool 5: Bristol v Leeds Carnegie, Gala v Wales 1
Pool 6: Cornish Pirates v Ulster Ravens, Jersey v Ayr
Round 2 -
Pool 1: Ealing Trailfinders v Wales 3, Moseley v Leinster 'A'
Pool 2: London Scottish v Edinburgh Academicals, Wales 2 v London Welsh
Pool 3: Bedford Blues v Wales 4, Connacht Eagles v Rotherham Titans
Pool 4: Nottingham v Munster 'A', Stirling County v Plymouth Albion
Pool 5: Leeds Carnegie v Gala, Wales 1 v Bristol
Pool 6: Ulster Ravens v Jersey, Ayr v Cornish Pirates
Round 3 -
Pool 1: Moseley v Ealing Trailfinders, Leinster 'A' v Wales 3
Pool 2: Wales 2 v London Scottish, London Welsh v Edinburgh Academicals
Pool 3: Connacht Eagles v Bedford Blues, Rotherham Titans v Wales 4
Pool 4: Stirling County v Nottingham, Plymouth Albion v Munster 'A'
Pool 5: Wales 1 v Leeds Carnegie, Bristol v Gala
Pool 6: Ayr v Ulster Ravens, Cornish Pirates v Jersey
Round 4 -
Pool 1: Ealing Trailfinders v Moseley, Wales 3 v Leinster 'A'
Pool 2: London Scottish v Wales 2, Edinburgh Academicals v London Welsh
Pool 3: Bedford Blues v Connacht Eagles, Wales 4 v Rotherham Titans
Pool 4: Nottingham v Stirling County, Munster 'A' v Plymouth Albion
Pool 5: Leeds Carnegie v Wales 1, Gala v Bristol
Pool 6: Ulster Ravens v Ayr, Jersey v Cornish Pirates
Round 5 -
Pool 1: Leinster 'A' v Moseley, Wales 3 v Ealing Trailfinders
Pool 2: London Welsh v Wales 2, Edinburgh Academicals v London Scottish
Pool 3: Rotherham Titans v Connacht Eagles, Wales 4 v Bedford Blues
Pool 4: Plymouth Albion v Stirling County, Munster 'A' v Nottingham
Pool 5: Bristol v Wales 1, Gala v Leeds Carnegie
Pool 6: Cornish Pirates v Ayr, Jersey v Ulster Ravens
Round 6 -
Pool 1: Ealing Trailfinders v Leinster 'A', Moseley v Wales 3
Pool 2: London Scottish v London Welsh, Wales 2 v Edinburgh Academicals
Pool 3: Bedford Blues v Rotherham Titans, Connacht Eagles v Wales 4
Pool 4: Nottingham v Plymouth, Stirling County v Munster 'A'
Pool 5: Leeds Carnegie v Bristol, Wales 1 v Gala
Pool 6: Ulster Ravens v Cornish Pirates, Ayr v Jersey
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