Collectors are expected to fight determinedly over the result of a drunken encounter between the two at an east London art exhibition in the early 1990s.
Hirst produced Dantrolene, valued at £400,000 to £600,000, in response to Stewart's song "Damien Save Me".
Hirst dedicated the 1994 work on the reverse: "Being God (for Dave)".
The vast 150.2 by 155.25cm work is a prime example of the spot paintings that have been a constant theme throughout Hirst's career.
They often perform well at auction.
In October 2010, a much smaller spot work by Hirst sold for £127,250 at Sotheby's, far above its £90,000 high end estimate.
Sotheby's Alex Branczik told the UK's Guardian newspaper the work is "one of the largest of its kind to come to the market for several years", adding that it is "a very rare thing".
Commenting on Hirst, Stewart said: "He reminds me of the Joker in Batman. Electric, turned on, alive. He'll talk for hours, really get you buzzing. [He] says that you've got to cope with death before you can handle life."
Hirst is equally enamoured with Stewart, stating: "Dave is wacky and wonderful, all over the place. [He's] got all these things on the go - like one plus one equals five."
It is one of seven works Stewart is putting up for auction, including a piece by Gilbert & George.
Not everyone can own a Hirst but alternative investors looking for contemporary artists at more modest prices can find some exceptional bargains on the private market.
Sotheby's also plans to sell an Andy Warhol print of Blondie singer Debbie Harry at the same sale for an estimated £5.5m.
Paul Fraser Collectibles will reveal the results later this month.
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