Eddie Campbell is a genius. But don’t take my word for it, take Alan Moore’s. “Eddie’s is a genuine one-off talent, utterly idiosyncratic and personal,” he says. Or perhaps Neil Gaiman’s: “The man’s a genius, there’s an end to it.”

If you don’t know Campbell by name, you’ll know his comics: most famously, he was Moore’s artistic collaborator on the tour-de-force From Hell, eventually adapted into a film starring Johnny Depp. But the Glaswegian artist produced a wealth of work both before and after From Hell. The Glaswegian artist’s oeuvre ranges from the ultimate punk-DIY – photocopying and distributing his autobiographical In the Days of the Ace Rock’n’Roll Club strips from a Southend bedsit in the 1970s – to drawing the likes of Captain America and Batman. But while his Marvel and DC work is proof that Campbell can do pretty much anything, it’s in the more experimental, creatively free projects that he seems to shine, no doubt informed by the punk rock publishing ethos of his early days: Bacchus, a series that plonks ancient Greek gods into the modern age, or The Lovely Horrible Stuff, a treatise on our relationship with money.

Moore is as effusive with praise as he was 30 years ago, when he first spotted Campbell’s Ace Rock’n’Roll Club strips and gave them a glowing review in Marvel’s magazine Daredevils. “Eddie’s style, both his loose, impressionistic line and his approach to storytelling, was fresh, exciting and like nothing anyone had ever seen before,” he says. “Luckily he had someone as insightful and perceptive as me to explain that to everybody.”

The Ace Rock’n’Roll Club, the series that caught Moore’s eye, were beautifully formed slices-of-life which introduced, as a part of the supporting cast, Alec McGarry. Alec was a cipher for Campbell, a fictional avatar through which Campbell could filter his own life, ranging from his punk years in Scotland to his sojourn on England’s south coast, to his first marriage and life in Australia. “His appreciation for the sensory phenomena of ordinary existence, as rich as Henry Miller’s, made his autobiographical narratives into instant classics, streets ahead of the largely self-absorbed comic-strip memoirs that were to follow,” says Moore.

Speaking from his “writing cabin” in New York state, Gaiman points out a shelf opposite his desk that contains only books he considers incredibly important; a collected edition of Campbell’s Alec strips sits on it. “I couldn’t compile a list of the most important graphic novels of the 20th century without including Alec on it. Eddie’s style is … ” He thinks. “Well, he doesn’t really have one single style. He’s an original. He draws from life.”

Saying Campbell doesn’t have a style may sound like a slight – it isn’t. The Alec comics are, as Rolling Stone once described, “impressionistic and quotidian; a shockingly hard combination to pull off”. Even his Captain America work is recognisably Marvel, if also feeling curiously retro; the line-drawn panels in his Bacchus stories seem deceptively simple but, on scrutiny, are incredibly detailed; his art on From Hell is scratchy and unnervingly shadowed.

From Hell would not have been as interesting if Eddie Campbell had not drawn it, says Gaiman – a position even Moore agrees with. It’s Campbell’s “effortless” ability to depict authentic, everyday life, he says (a useful trait when drawing a comic about Jack the Ripper). “His matter-of-fact approach to the most potentially sensational of subject matter was just what was needed, simultaneously getting rid of all the tawdry manipulation that comes with standard visual horror fare, and replacing it with a sense of the commonplace that made the crimes depicted much more honestly horrific and appalling,” he says.

Like Moore, Gaiman championed Campbell’s work long before he met him, reviewing Alec for the adult magazine Knave, for which Gaiman wrote under a pseudonym. Later, they’d work together, on a story featuring Will Eisner’s character The Spirit. Even later, they’d become friends, with Gaiman dedicating a book to Campbell’s daughter, Hayley, and introducing Campbell to Audrey Niffenegger, author of The Time Traveller’s Wife. The pair married in 2016 and live in Chicago. “It couldn’t have happened to a nicer pair of people,” says Gaiman.

Campbell’s chameleon style is perhaps most evident in his new joint creation with his wife: Bizarre Romance is a mixture of prose pieces by Niffenegger, adaptations of her stories by Campbell, and original comic strip collaborations by both of them, all varying wildly in tone and form.

Is this the book that will finally bring Campbell stardom? Gaiman initially disagrees: “I never understood that view. In my personal pantheon of comic creators from the last 35 years, Eddie Campbell is right up there on Mount Olympus.” Later, he rethinks this: “I never expect the world to catch up with him. Maybe in 200 years from now when people look back at the world today, they’ll say that Eddie Campbell was chronicling it best.”

• Bizarre Romance by Audrey Niffenegger and Eddie Campbell is published by Jonathan Cape, at £16.99. It is available for £12.55 from the Guardian Bookshop.