Anomaly beat FCB Inferno, Grey and Mother to win the contest, which began in April.
Anomaly is charged with creating an integrated brand campaign for Cancer Research UK that will go live in December 2015.
Abbott Mead Vickers BBDO had worked with Cancer Research UK on its brand campaigns for the past five years but did not pitch for the account. The agency continues to collaborate with the charity on a project basis.
Camilla Harrisson, Anomaly’s chief executive, said: "We are elated. It’s a massive privilege and a huge responsibility. I can’t think of a brief which is more demanding of brilliant work that overperforms."