The teams, from the four home nations, are drawn in eight pools of four, with only the pool winners qualifying for the knockout stages.
In addition to 12 teams being added to the competition, another format switch sees clubs now face each other home and away in the pool stages.
The participating teams comprise the 12 teams from the RFU Championship; the development teams from the four Irish provinces; the top four teams from Scotland's RBS Premier Division 1 last season; and the 12 teams from Wales' Principality Premiership.
Joining the competition for their debut season are Bridgend Ravens, Bedwas, Stirling County, Carmarthen Quins, Dundee HSFP, Newcastle Falcons, Jersey, and Gala.
The competition will now take place over nine rounds and will align with ERC weekends. Competition Manager Chris Burns said: "These changes reflect the commitment of all the Unions and clubs to help grow the profile of the B&I Cup within the rugby calendar."
The pool games will take place as follows: Round 1 - 12-14 October; Round 2 - 19-21 October; Round 3 - 7-9 December; Round 4 - 14-16 December; Round 5 - 11-13 January; and Round 6 - 19 January.
The quarter-finals will be played the weekend of 5-7 April; the semi-finals 26-28 April; and the final Friday 17 May (TBC).
2012-13 British & Irish Cup - Pools
Pool 1 - Bristol Rugby, Bridgend Ravens, Cardiff and Ulster
Pool 2 - Bedford Blues, Bedwas, Neath and Stirling County
Pool 3 - Carmarthen Quins, Dundee HSFP, Cornish Pirates and Swansea
Pool 4 - Connacht, Cross Keys, Newcastle Falcons and Newport
Pool 5 - Jersey, Leeds Carnegie, Leinster and Pontypridd
Pool 6 - Gala, Llanelli, London Scottish and Moseley
Pool 7 - Aberavon, Munster, Plymouth Albion and Rotherham Titans
Pool 8 - Doncaster Knights, Llandovery, Melrose and Nottingham Rugby
This will be the fourth year of the competition with Cornish Pirates, Bristol Rugby and Munster previous winners.