The My Hero hitmakers also triumphed over Florence + the MAChine, Bon Iver, The Black Keys, The Cure, The Killers and the reunited Stone Roses to claim the top prize.
Of Monsters and Men were awarded Best Newcomer ahead of acts like Alabama Shakes, rapper Azealia Banks and 2012 Mercury Prize winners Alt-J, while singer Lykke Li went home with the title of Best Festival Anthem for her hit track I Follow Rivers.
The Best Major Festival prize was handed to the organisers of electronic music gathering Tomorrowland, which is held in Belgium.
The winners, which were decided by a combination of votes from the public and industry experts, were announced at a ceremony in Holland on Wednesday (09Jan13).
The Foo Fighters' win comes weeks after frontman Dave Grohl was forced to deny speculation the group was on the verge of splitting after ending an extensive world tour by announcing he wasn't sure when the bandmates were going to play again.