Plans show a food store, hotel, two fast food restaurants, pub and petrol station. The authority said that subject to the plans being approved, work would start in spring next year with a completion target of August 2007. The Scarlets would then leave Stradey Park, which has been home to the team since 1879.
Club chief executive Stuart Gallacher said the move would secure the future of the Scarlets. He said: "In the professional era you can't do without the best facilities on and off the field so this project is essential to help us realise our ambition.
"It will also provide the people of Carmarthenshire with outstanding sports facilities on their doorstep."
The scheme includes a 15,000 capacity stadium, indoor training barn, athletics track with 500-seater stand, floodlit practice pitch and gymnastics facility. Council executive board member Clive Howells said: "This is a very ambitious development and we are pleased to be making such good progress.
"We still have a lot of work to do before we are in a position to finalise the scheme, but it is proceeding very well."