The acquisition is worth an initial £5 million upfront, with yearly earnout targets understood to be based on performance criteria over five years.
Marvellous, founded five years ago by the joint managing directors Jon Carney and Paul Seaton, has gross assets worth £0.8 million.
The agency's mobile services include strategy, media planning and buying, creative and technology services. Clients include Vodafone, Coca-Cola, Adidas, Reebok and GlaxoSmithKline.
Marvellous will sit in the Isobar network as an individual brand, but will collaborate with other network companies, such as the online media agency Diffiniti, on projects.
Nigel Morris, the chief executive of Isobar, said the deal reflected the network's commitment to mobile as a key growth channel.
Morris said: "We believe mobile will become an important medium, and will play an increasing part in all brand communications. It's still at the early stages of its development around the world, but there is no doubt it is going to be the primary point of access to the internet."
Morris said the network has plans to develop the UK-based agency in other markets, including the US and Asia. "We have ambitions to own the mobile space with Marvellous there as the pioneers," he said.