The decision was taken by Scottish Rugby after consultation with representatives of the Premiership Forum.
The intended changes to the competition will mean that six fixtures will be played in the competition before Christmas, amendments which have been met with resistance from Scottish Rugby. The governing body is concerned that having clubs competing in the competition would compromise the integrity of their flagship club competition, the BT Premiership.
"In light of the changes to the British & Irish Cup competition structure, our four qualified teams - Melrose, Gala, Ayr and Heriot's - will not participate in the 2014-15 competition," said Colin Thomson, Scottish Rugby's director of rugby operations.
"Discussions over the competition structure have been difficult and we have done everything in our power to try to influence a solution that would meet the needs of all participants. Regrettably this has not been achieved and the B&I Cup pool dates have been set for two blocks of three fixtures either side of the Autumn International window.
"Given this, we simply could not support six B&I Cup games in the first half of the season as this would have a significant impact on the integrity of our own BT Premiership competition. Scottish Rugby will continue to work with its clubs to find suitable cross-border opportunities."
The decision to withdraw from the competition has been articulated with more frustration by the clubs. However, there has also been a determination to make the best of an unfortunate situation.
"The British & Irish Cup has been a really important tool in player development so while we're disappointed that negotiations have not concluded in a manner which would enable our continued involvement, we recognise that first of all we have to maintain the quality and integrity of our own competition, the BT Premiership," said Mike Dalgetty, the director of rugby at Melrose.
Billy McHarg, the Ayr president, last night echoed that sentiment. "The B&I Cup was an important tournament for building the quality of teams and raising playing standards at Ayr, particularly after reaching the quarter-finals against Bristol three years ago and notable wins against Ulster and Jersey this season," he said.
"Our drive to do that goes on in the BT Premiership and we look forward to working to find other cross-border opportunities."