Their record, Dead, beat 11 other albums from acts including Damon Albarn, Bombay Bicycle Club and bookmakers’ favourite, FKA Twigs.
“We’ll take it in our stride,” said band member Graham ‘G’ Hastings.
“We always wanted to make something bigger than the city we were living in.”
The winner of the £20,000 prize was announced by DJ Nick Grimshaw at the Roundhouse in north London.
“Young Fathers have a unique take on urban British music, brimming with ideas – forceful, unexpected and moving,” said Simon Frith, chair of this year’s judging panel.
The trio, who met at an under-16s hip-hop night, have developed a reputation for making a unique blend of music, utilising diverse influences that reflect their different backgrounds.
Massaquoi is originally from Liberia, Scots-born Bankole has Nigerian parents, while Hastings hails from Drylaw in the north of the city.
Dead was the second lowest selling album on the shortlist, having sold just 2,386 copies since its release in February.