The agency landed the account following a pitch against JWT London, WCRS and Wieden & Kennedy in a process handled through the AAR.
Heineken, which acquired the brand in 2008, called the review in January. St Luke's, the previous incumbent on the account, did not repitch but continues to handle ad duties on Bulmers' sister brand, Strongbow.
Earlier this week, Heineken appointed Work Club to handle the global digital advertising for its Strongbow Gold variant.
Adam & Eve has alcohol experience through its work for the lager brand Foster's, which is also brewed in the UK by Heineken.
Gareth Turner, the senior brand manager at Bulmers said the appointment marked "an exciting new chapter in the brand’s history in the knowledge that the agency will bring a fresh perspective and strong ideas to Bulmers, along with a creative reel that is second to none".
James Murphy, the Adam & Eve founding partner added that the campaign created by his agency would "assert the authenticity" of the Bulmers brand.