Fosse, who started the week as a rank outsider, with Ladbrokes offering odds of 100-1, saw his odds dramatic shorten to just 9-1 over the last few days before the announcement on Thursday, as bookmakers took in a sudden surge of bets in his favour.
Alice Munro had been the bookies' second favourite, with odds of 4-1 on Tuesday afternoon, just below its 5-2 Ladbrokes was offering for Haruki Murakami, the favourite.
Munro, described as "the master of the contemporary short story", is only the 13th woman to ever win the prize.
"It's wonderful for me. It's wonderful for the short story," she said when she was rung after the award was announced.
Fosse, 54, a post-modernist known for minimalist dialogue and repetitive themes, is widely regarded as one of the world's best living playwrights.