The move would give the premium-quality produce the same prestige and protection as Scotch Lamb, Arbroath Smokies, Stornoway Black Pudding and Scottish Salmon.
The application, if successful, would see the potatoes gain Protected Geographical Indication (PGI) status under the EU's Protected Food Name (PFN) scheme, giving protection against inferior copies.
It would mean only selected potatoes grown in the region and harvested in season - May to July - could be branded as Ayrshire Earlies.
The application has been developed by Ayrshire growers including the Girvan Early Growers, Scotland's Rural College and Airdrie-based Albert Bartlett, who supply the potatoes through the Scotty Brand.
The UK and Scottish governments are supporting the move to register the vegetables under the name Ayrshire Early New Potatoes and Ayrshire Earlies.
The sweet potatoes, which do not have to be peeled, have been grown in Girvan since the 1850s.
Ayrshire potatoes in the late 19th and early 20th century were primarily harvested by migrant Irish workers known as "tattie howkers". In 1910 about 1,000 such workers were employed in the Girvan area alone, and special trains were laid on to transport the crop around the UK.
The move has the backing of Scottish Secretary Alistair Carmichael, who will team up with Owen Paterson, the Environment Secretary, to push for the potatoes to be protected. The application will now be subject to a national consultation and will be assessed by the Department for Environment, Food and Rural Affairs, before being submitted to the European Commission if issues arising are resolved.
Mr Paterson said: "It's great news. The Department for Environment, Food and Rural Affairs will work closely with the region's farmers to ensure that this application is processed as soon as possible through our negotiations with the EU.
"The UK's iconic and unique regional food producers have been incredibly successful in supporting and protecting Protected Food Names. Scotch Beef and Lamb alone already contribute £78 million to the economy every year, much of this through export deals secured by the UK Government."
First Minister Alex Salmond added: "Ayrshire Early New Potatoes are well sought after and achieving PGI status will provide a 100 per cent guarantee of the product's authenticity for consumers at home and abroad.
"Local producers have experienced benefits from the PFN scheme by protecting their products from imitation. It's also a great accolade and means we can promote them more effectively.
Meanwhile, the Scottish Government has outlined its plans to increase access to quality food. These include the creation of a Scottish Food Commission and local "champions" to promote good food choices to consumers and enlist the support of retailers and producers.