The Marketing Group, which is chaired by serial entrepreneur Jeremy Harbour, floated on NASDAQ's Nordic stock exchange, NASDAQ First North, in Stockholm in June.
Graham claims the company, which has a €100m valuation, could become a €1bn business.
The group owns 19 agencies in Singapore, Australia, the US and the UK and is targeting other "mature, profitable, debt-free" agencies.
Graham's decision to join The Marketing Group marks an abrupt change of direction as he told ±±¾©Èü³µpk10 in September that he was working on plans to found his own marketing services group, dubbed Project Oak, with the aim of getting £100m in backing from private equity investors to buy small agencies and scale up.
He said he decided to join The Marketing Group because it has similar ambitions and has already raised cash while he has a "pipeline" of planned acquisitions that he can bring to the group.
Harbour, a Briton who has worked in Spain and Singapore, is a little-known figure in the marketing and advertising industry but has run Unity Group, a small private equity house.
He claims The Marketing Group is "the world’s leading digital marketing and advertising agglomeration".
The group floated on NASDAQ in Stockholm because it maintained that a smaller plc would have more liquidity than on the London stock market, despite TMG being registered and incorporated as a company in the UK.
TMG's share price has been volatile. It was priced at €1 on its debut, rose to €9, before falling back to €3.50.
Graham, who previously worked for Omnicom's digital shop Weapon7 and WPP's Rainey Kelly Campbell Roalfe/Y&R digital offshoot Saint, said: "It's a disruptive new model which is totally aligned to my beliefs that there is a better way than the lumbering bureaucratic monoliths who currently dominate the space.
"This model encourages entrepreneurs to continue to be entrepreneurial. We want our agencies to thrive within our light touch infrastructure that encourages them to maintain all the characteristics that made them the great agency they are today, forever more. "How many times do we see the networks sucking in a cool agency only to then homogenise it? So many great agency brands either disappear or become pale reflections of their former selves.
"This model is different and I believe it is the future for independent agencies who want to realise some value without feeling like they have sold their soul."
He believes there is gap in the market for a group that can support agencies with an operating profit (EBITDA) below £1m that would be too small to appeal as acquisitions to the big holding groups.
TMG's agencies include One9Ninety and Black Marketing in Singapore, The Lead Generation Company in Australia, Wilkin Marketing and TDA Group in America, and Nice & Polite, Slingshot Sponsorship and Ranieri Public Relations in the UK.
Harbour, the executive chairman of The Marketing Group, said Graham's "experience building and managing digital agencies, together with his industry knowledge and relationships, will be immensely valuable to The Marketing Group", adding: "We are confident the company will continue to grow from strength to strength with his vision and guidance."
Graham was CEO of Weapon7 from 2011 to 2013. Omnicom moved it into Abbott Mead Vickers BBDO and dropped the brand name a year later.
He has most recently been working at Cact.us, an agency consultancy, and is chair of the British Interactive Media Association.
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