The agency won a final shoot-out against WWAV Rapp Collins, after Euro RSCG and Oglivy Advertising were knocked out an earlier stage of the pitch process.
The account includes online and off-line communications and is split into four markets: the Nordic region, western Europe, eastern and central Europe, and southern Europe. The pitch was overseen by Agency Assessments International.
Unibet is expected to launch a heavyweight marketing campaign in the UK before the end of the year, following the relaxation of advertising regulations in the wake of the Gambling Act 2005, which came into effect on September 1 this year.
A spokeswoman for Unibet declined to comment.
Unibet was founded 10 years ago and is one of Europe's largest online operators, with more than 1.7m customers.
The company courted controversy earlier this year, when it emerged that its sponsorship of the Tour de France cycling team, Green Cycle Team, contravened French law.
In France, foreign-owned gambling firms are banned from sponsoring sports teams. Unibet slammed the decision to ban the team from the Tour de France as a "scandal" and pointed out that French horseracing betting firm, Pari Mutuel Urbain, and French lottery operators, La Francaise des Jeux, were two of the main sponsors of the event.