The deal will see Marc Cave, the founder and owner of Drugstore, joining the Erasmus co-founders, Graeme Dignan and Ross Cairns, as an owner-manager of the enlarged company.
The merged company has also appointed Jon Wilkins, a co-founder of Naked Communications, as a non-executive director.
Erasmus works with clients including Coca-Cola, and has a stake in the Coke-owned energy drink Relentless, which it helped to create as a competitor to Red Bull.
According to Cave, Drugstore will add its experience in advertiser-funded programming and media to Erasmus' heritage of developing FMCG products.
Dignan said: "Very rarely do we find people and businesses that share the same view of the world, and the same desire to do great work that disrupts conventions to build culturally relevant brands."