The London trio won the critics' choice award for their debut album xx, after competing against Paul Weller, Mumford & Sons, Foals and Dizzee Rascal, amongst others.
They collected the £20,000 winner's cheque from Jools Holland at the ceremony at London's Grosvenor House Hotel tonight.
xx has been met with critical praise since its release in August 2009, already selling 125,000 copies prior to the competition. Despite being strong contenders to take the prize, the band said that they had not expected to be celebrating a victory.
The prestigious award, now in its 18th year, is voted for by a panel of music industry executives and experts. Acts traditionally experience a surge in album sales following the contest.
Previous Mercury Prize winners include Elbow, Arctic Monkeys, Pulp and this year's competitors Weller and Rascal.