Click here to listen to a sample of Mark Ronson's remix

Bob Dylan, the dance remix, far from causing outrage, has gone down a storm.

DJ Mark Ronson’s version of the 1966 song Most Likely You Go Your Way (And I’ll Go Mine) had its world premiere on BBC’s Radio 1 and proved so popular that the DJ Zane Lowe played it twice.

The track was expected to provoke howls of protest similar to those seen when Dylan “went electric” in 1966. Instead callers phoned the station to voice their approval and less than an hour after its first airing, Radio 1 replayed the track.

After years of rejecting all offers to remix his catalogue, Dylan, 66, decided to allow Ronson to rework the song as a way of introducing his generation-defining work to a new teenage audience.

The London-born Ronson is one of the world’s hottest producers, having worked with Amy Winehouse and Lily Allen. He recently turned a song by the Smiths into a pop hit.

Dylan’s record company hopes the early interest in the Ronson remix could signal the beginning of a Dylan revival. When Elvis Presley’s estate sanctioned a remix of his A Little Less Conversation in 2002 it became a global No 1 and revitalised interest in “the King”.

Mike Smith, the managing director of Columbia Records, told The Times: “It is the first time Bob has agreed to anything like this. We want to bring his music to an audience unfamiliar with Dylan in a similar fashion to the Elvis campaign.”

Ronson and Smith were invited to trawl through the entire Dylan catalogue for a suitable track to reinvent. Smith said: “We hit on You’ll Go Your Way because it already has a great rhythmic breakbeat. It’s also got a timeless, universal lyric."

Ronson said: “It’s the first time Bob Dylan has given anyone the original multi-tracks of his songs to do remixes. I’m a huge Dylan fan, so it’s a great honour, along with the fact that he heard it and approved it, because, as you imagine, he’d be quite picky.”

Dylan is enjoying a creative resurgence with Modern Times, his 44th album, topping the American charts. His never-ending tour continues and his puckish radio show, which features classic folk, jazz and blues, has become a BBC Radio 2 hit.

He is not the only rock veteran to succumb to the remix temptation. The Beatles’ Love, the soundtrack to a Las Vegas stage show, comprises elements of their best known songs stitched together under the direction of Sir George Martin. Their lawyers were less pleased when the DJ Danger Mouse created The Grey Album by mixing raps from Jay-Z’s Black album with the Beatles’ White Album. The acclaimed results were removed from the public domain.

The Ronson remix is released digitally on September 17 and physically on September 24 and the track will be included on a 51-track, three-CD Dylan retrospective, to be released on October 1.

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