The pitch kicked off in July this year and was overseen by Andy Smith, the group managing director of Lactalis McLelland, which owns the President cheese brands.
It is unclear how Burkitt DDB's merger with sister shop DDB London, a move expected to take place next year, will impact on the business.
The incumbent on the UK account, Publicis, resigned the Emmental account in August this year as part of a "mutual agreement".
Globally, President uses a number of network shops, including Ogilvy & Mather and DDB in Paris.
President is second to the brand leader, Leerdammer, which invests significantly in television and broadcast sponsorship.
Julian Calderara, the chief executive of Burkitt DDB, said: "We are delighted to have won President.
"The British public has a growing love affair with good food; authentic, high-quality products, such as President's, are very much what people are looking for."
He added: "We see great potential in becoming partners with this ambitious and exciting company."