The agency beat WWAV Rapp Collins, Ogilvy and Euro RSCG in a review overseen by Agency Assessments International.
TBWA will now work on a European campaign, expected to break in the UK next year, to raise awareness of Unibet and drive traffic to its website.
It is unclear whether the work will include TV - although the Gambling Act 2005 allows gambling companies to advertise on television in the UK, legislation in Europe varies.
The £20 million campaign will initially launch in France, Spain and Italy and continue into eastern European countries early next year. Unibet is expected to invest half of its budget online.
Earlier this year, the company tried to raise its profile by sponsoring the Green Cycle Team in the Tour de France. However, it was later forced to pull out of the deal as French law bans foreign-owned gambling firms from backing sports teams.
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