The agency defeated the 14-year incumbent Abbott Mead Vickers BBDO in a three-way final shoot-out that also included Grey London.
VCCP and WCRS were also included in the process, but were knocked out in an earlier round.
The review was handled by Oystercatchers and Camelot commercial director Richard Bateson.
Camelot called the review in February in a bid to "reinvigorate the brand" and highlight the "unique role it plays in society."
Adam&Eve/DDB would not comment, while Camelot said it is not in a position to comment as the process is "still ongoing".