The 75-year-old was controversially handed the prestigious accolade earlier this month for “having created new poetic expressions within the great American song tradition”.
The Swedish Academy said Dylan, who is due to show a collection of art in London in November, acknowledged the prize for the first time this week in a phone conversation.
They said he told Sara Danius, Permanent Secretary of the Swedish Academy: “I appreciate the honour so much.”
And he said: “The news about the Nobel Prize left me speechless”
DOWNLOAD THE SCOTSMAN APP ON ITUNES OR GOOGLE PLAY After failing to comment on the award immediately after it was announced, Dylan was called “impolite and arrogant” by an official from the Academy.
But in an interview with the Daily Telegraph he said he “absolutely” wants to attend December’s Nobel Prize Award Ceremony “if it’s at all possible”.
He told the newspaper being awarded the prize was “hard to believe”, adding it was “amazing, incredible.”
“Whoever dreams about something like that?”
Dylan became the first American to win the literature prize since Beloved author Toni Morrison in 1993.
His win was praised by literary figures and critics, with a leading academic hailing him as the Tennyson of our times.
Professor Seamus Perry, chairman of the English Faculty at Oxford University, described Dylan as “one of the greats”, saying: “He is, more than any other, the poet of our times, as Tennyson was of his, representative and yet wholly individual, humane, angry, funny, and tender by turn.”
The decision was not received well by everyone, with Trainspotting author Irvine Welsh labelling it an “ill conceived nostalgia award”.
The Scottish novelist and playwright tweeted: “I’m a Dylan fan, but this is an ill conceived nostalgia award wrenched from the rancid prostates of senile, gibbering hippies.”
Born Robert Zimmerman on May 24 1941, in the backwaters of Minnesota, he reinvented himself as folk singer songwriter Bob Dylan.
He famously sparked controversy by shifting to electric guitars in 1965 and was criticised by leading members of the folk movement for moving away from political songwriting.
In 2008, the singer-songwriter won the Pulitzer Prize for his contributions to music and American culture.
His latest album, Fallen Angels, released in May was praised by critics - with Rolling Stone saying: “His phrasing remains spectacular, sometimes heartbreaking, sometimes hilarious, and the playing is sublime.”
The Times They Are A-Changin’ singer, who has sold more than 110 million records, has also produced paintings and drawings since the early 1960s.
He will bring his vision of American landscapes and urban scenery to Britain with a new collection of his art set to go on display at the Halcyon Gallery in central London next month.
The show will feature watercolours and acrylic works of downbeat motels, forgotten fairgrounds and American landmarks including The Green River, which runs through Wyoming and Utah, take from his travels across America.
His exhibition, The Beaten Path, will open on November 5 at the Halcyon Gallery and run until December 11.
The six Nobel prizes will be handed out at a ceremony on December 10.