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.
President Obama said the honour was "well-deserved".
Dylan's songs, such as "Blowin' in the Wind", "The Times They Are a-Changin'", "Subterranean Homesick Blues" and "Like a Rolling Stone" captured a spirit of rebellion, dissent and independence.
More than 50 years on, Dylan is still writing songs and is often on tour, performing his dense poetic lyrics, sung in a sometimes rasping voice that has been ridiculed by detractors.