The Anglo-Welsh Cup is to be replaced by a new competition next season involving all 12 Premiership clubs.
The Premiership Rugby Cup will carry prize-money of more than £500,000 and see teams competing in three pools of four.
The first two pool rounds will start on the final weekend of October, and the last two in late January.
Three pool winners and best runner-up will progress to the semi-finals, while group stages will also include a 'Derby day' round, Premiership Rugby said.
Welsh regional teams end their 13-year involvement through the Anglo-Welsh Cup, with an emphasis in Wales now being put on a new under-23 competition.
"We are sad that our friends in the Welsh regions will not be involved next season, but we have been discussing for some time that they need to move to a new structure, prioritising an under-23 format," Premiership Rugby chief executive Mark McCafferty said.
"The cup has been a highly-successful competition in recent years in helping develop the best new Premiership and England players, in front of big crowds and television audiences.
"The focus on new playing and coaching talent will continue in the new cup format with young players and coaches experiencing the challenge of bigger crowds and TV exposure."
A spokesperson for Pro Rugby Wales added: "The review of development structures and processes we have undertaken together with the WRU (Welsh Rugby Union) over the last 12 months has clearly illustrated the need for us to focus on our 18-23 years player development through a dedicated under-23 competition.
"This unfortunately means we will no longer have the resources to be able to compete in the Anglo-Welsh Cup.
"We have a great working relationship with the English clubs and Premiership Rugby, and hope we can work together in the future as the game continues to evolve."