Last month the board used powers granted under the Licensing (Scotland) Act to refuse permission to Tesco, Asda, Morrisons, the Co-op and Marks & Spencer to increase their drinks displays.
The decision was made because retailers could not prove their plans would promote public health, a condition which forms part of Scottish licensing law.
The board was advised the ruling was unlikely to survive an appeal, and this week it reversed its decision.
Board chairman Stephen Dornan said, while its original stance had been “entirely justified”, the law was “flawed” because it did not allow councillors to get endorsement for their health-based objections.
The Wine & Spirit Trade Association welcomed the U-turn. “We always thought licensing laws were being misinterpreted,” said a spokesman.