Chris Brown, Asda's agricultural strategy manager, said the deal would see the supermarket "go back to its roots" by forming a direct relationship between the farmer and the store group which is also based in Leeds.
Reacting to the council's decision on Thursday evening, local farmer Glyn Morgan, chairman of action group Save Our Common Mountain Environment (Socme), told BBC Radio Wales the energy firm's plan was "total destruction of an environment".
Aberystwyth student Emyr Llewelyn, farmer's son Owain Williams, and former RAF military policeman John Albert Jones, formed the shadowy group Mudiad Amddiffyn Cymru, the Movement for the Defence of Wales.