Two whip-thin creatures, blinking into the sunlight for an old man on the boardwalk, smile softly from the cover of this moving memoir. Taken at the Coney Island funfair in 1969, the picture shows Patti Smith and Robert Mapplethorpe, a pair of 22-year-old lovers celebrating two years together.
“It was our good fortune that this moment in time was frozen in a box camera," Smith writes. "It was our first real New York portrait. Who we were."

Thus her account of a relationship between two remarkable artists stems, rather fittingly, from a photograph. The girl from New Jersey who would fuse poetry with rock'n'roll and the lapsed Catholic boy who became a feted, controversial photographer met by chance shortly after Smith arrived in New York on a bus in 1967. They quickly became lovers, and each other's muse, breaking up only when Mapplethorpe came to terms with his homosexuality.

Their intense kinship survived, however, and before Mapplethorpe's death in 1989, Smith promised that one day she would tell their story. That it has taken her 21 years to do so suggests quite how demanding and wrenching the task must have been.

But as Just Kids whirrs magically into life, one worries that it is merely an exercise in myth-making. It starts with Puccini's Tosca singing an aria about love and art as Smith finds out about the death of her soulmate. Then we feel the full blast of her overwrought prose. She writes of her first child, given up for adoption when Smith was still a teenager, as having been "born on the anniversary of the bombing of Guernica". A curtain hung by Mapplethorpe in their first flat "harmonised with my own gypsy elements", while Horses, the 1975 album that made Smith's name - and Mapplethorpe's reputation, thanks to the shot of his ex on the sleeve - is not a record, but an "aural sword sheathed with Robert's image".

Smith depicts the pair as the Big Apple's answer to Rimbaud and Verlaine, the Fates bringing them full purses and silk-laced shoes, as they penny-pinch for food and deal with lice on the pillow. They are, one senses, a couple of whom you could tire very quickly. But her writing becomes warmer as their story progresses, narrating her and Mapplethorpe's extraordinary journey from a tiny flat in Brooklyn to the Chelsea Hotel, and encounters with some of the period's countercultural luminaries.

We watch Smith meeting Jimi Hendrix on a club stairwell and eliciting his sympathy when she is too "chicken" to go in (a memory that adds a new layer of meaning to her version of Hendrix's "Hey Joe"). Asked to fake shooting up heroin for a friend's artwork, she reacts with horror - her only brush with drugs, up to that point, having been a spiked drink. Her small-town mind also fails to see through Mapplethorpe's obsessions with sailors and men in tight leather, which ought to have suggested interests outside the couple's bed. But as it reveals her more innocent side, this fierce girl's writing gains a deeper power.

She also recognises the arrogance of youth - especially when she remembers being present as Kris Kristofferson played "Me and Bobby McGee" to Janis Joplin for the first time, in a room littered with bottles of Southern Comfort. Back then, she was "so young and preoccupied with my own thoughts that I hardly recognised them as moments" - an especially telling insight into Smith's character.

As time winds on, she and Mapplethorpe part as lovers but continue to share a loft, and the cast list keeps growing. Smith touches on relationships with the playwright Sam Shepard and the poet Jim Carroll, her first meeting with her mentor Allen Ginsberg - who initially assumes that she is a beautiful boy - and her friendship with Lenny Kaye, with whom she performed her debut poetry evening in 1971, and who later gave the Patti Smith Group its musical bedrock. These relationships are gently brushed over, however: Mapplethorpe's shadow looms too large for Smith to dwell long among other ghosts.

After all, Just Kids has a very different focus from other stories about rock stars and their lives before they became famous, such as Bob Dylan's Chronicles or Nowhere Boy, the film about John Lennon's adolescence. This is essentially a love story, and a reminder that the deepest relationships need not have perfect resolutions.

“We said farewell and I left his room," she concludes, ending the book as she began it, with the death of the man who gave her life. To Smith, Mapplethorpe still looked like "a sleeping youth cloaked in light", and this is how she wants us to remember him. "Of all your work," she tells him, as she tells us, "you are still your most beautiful."

Just Kids
Patti Smith
Bloomsbury, 304pp, £18.99