The 75-year-old rock legend received the prize "for having created new poetic expressions within the great American song tradition".
The balladeer, artist and actor is the first American to win since novelist Toni Morrison in 1993.
His songs include Blowin' in the Wind and The Times They are A-
Sara Danius, permanent secretary of the Swedish Academy, said Dylan had been chosen because he was "a great poet in the English speaking tradition".
The singer is due to perform later at the Cosmopolitan hotel in Las Vegas.
"Best words in best order"
Dylan - who took his stage name from the poet Dylan Thomas - had long been tipped as a potential prize recipient.
Few experts, though, expected the academy to extend the award to a genre such as folk rock music.
Former Poet Laureate Sir Andrew Motion is among those to have previously praised Dylan's lyrics, saying his songs "work as poems".
He told the BBC: "They're often the best words in the best order."