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 field advantage'.
RFU professional rugby director Rob Andrew commented: "The British & Irish Cup organising committee agreed that the reduction in clubs would make for a more competitive league competition.
"The regional play-offs are a positive way of ensuring an appropriate regional spread combined with the best teams representing Wales in the competition, while the top four finishers in the Scottish domestic leagues will be automatically included alongside the 12 RFU Championship clubs."
WRU gead of rugby Joe Lydon added: "The British & Irish Cup is a fantastic competition and the restructure will give four Principality Premiership clubs every chance of being highly competitive.
"It will again give Premiership and select regional players the opportunity to play in this cross-border tournament which is not only a great way to develop player talent but also an opportunity for the respective clubs to grow and test themselves.
"We firmly believe that the system of regionally based play-offs determining participation in the British & Irish Cup is the fairest way of selecting the best teams to represent Wales while reflecting the geography of Welsh semi-professional and professional rugby.
"Our clubs have more than held their own in this competition which sees them compete with full time, professional clubs and provinces, with Cross Keys reaching last season's final, Pontypridd reaching last year's semi-final and Llanelli reaching the quarters on three occasions.
"We are confident that this move will enhance our competitiveness in the British & Irish Cup and we look forward to some thrilling encounters in the battle for places come September."
2013/14 BRITISH & IRISH CUP STRUCTURE:
* 12 English RFU Championship clubs
* 4 Welsh Principality Premiership clubs
* 4 Irish provinces - Connacht Eagles, Munster 'A', Leinster 'A' and Ulster Ravens
* 4 Scottish teams - top 4 finishers in RBS Premier Division: Ayr, Gala, Stirling County and Edinburgh Academicals
Pool Stages -
* 6 pools of 4 teams 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 progress to knock-out stages, including two best runners-up
* 8 quarter-finalists ranked with teams ranked 1-4 having home advantage
* 4 winning quarter finalists progress to semi-final draw
* Winning semi-finalists progress to final