The band, led by drug-troubled Doherty, will release the single as they put the finishing touches to their second album, 'Shotter's Nation', the successor to 'Down in Albion', which was released at the end of 2005.
The special acoustic version of 'Delivery', which will not be officially released until September 17, will feature a B-side interview with the band discussing the new album. The vinyl is covermounted with the issue of NME, on sale September 12.
Early reviews of the new single have been positive, as the band struggles to put Doherty's drug troubles and split with supermodel girlfriend Kate Moss behind them.
Adam Ficek, Babyshambles drummer, said: "It's good to give NME readers the chance to hear 'Delivery' as a raw, stripped down demo, and also give an insight into how the song grew, developed and finally emerged into the actual finished album version."
The seven-inch single is likely to become a highly collectable item, featuring artwork by Doherty that is described as an exclusive "blood" drawing -- Doherty bizarrely uses his own blood to create images.
Earlier this year, some of his work including self-portraits and a bloodstained crucifixion scene, went on sale at London's Bankrobber gallery, with pieces reaching up to £16,000.
The Babyshambles exclusive vinyl single giveaway follows the successful White Stripes vinyl giveaway of the band's 'Rag and Bone' track with the NME in June.
Conor McNicholas, NME editor, said: "Yet again NME is leading the music and publishing industries by creating big release events to excite music fans. Following on from the White Stripes 'Rag and Bone' single, this is once more something really special.
"Pete is very close to our hearts and we're made up to be working with Babyshambles and the guys at Parlophone in releasing this unique track. Another instant collectors' item."