In early 1969, Andy Warhol agreed to design an album cover for the Rolling Stones.

The band’s frontman, Mick Jagger, wrote Warhol a letter about the project, telling the famed artist, “The more complicated the format of the album, e.g., more complex than just pages or fold-out, the more f–ked-up the reproduction and agonizing the delays.”

Warhol ignored this, creating one of the most complex and memorable album covers in rock history for “Sticky Fingers,” the 1971 album that took the Stones from stars to legends.

The cover of “Sticky Fingers” — which will be rereleased on Tuesday, remastered and featuring alternate takes and live versions of Stones classics — is a straight-up crotch shot.

The initial release featured a real zipper on the cover — when you pulled it down, you saw the model’s underwear.

Given that Jagger was regarded as the sexiest man in rock, it was commonly assumed to be his crotch. But the true identity of the well-endowed cover model has been a mystery for more than 40 years.

It all began when Warhol arranged to photograph several men from the waist down. After the photo shoots, he never told anyone the identity of the man on the cover, or even whether the jeans model and the underwear model were the same person.

While the model is definitely not Jagger, many people were under the impression that it was actor Joe Dallesandro, who starred in several Warhol films. But those who were in Warhol’s inner circle say otherwise.

Glenn O’Brien was the editor of Warhol’s Interview magazine. He says that Warhol photographed several men for the cover and he is “100 percent certain” that the inside photo — the one of a man in underwear — is him.

“I knew it was me because it was my underwear!” he tells The Post. “[Warhol] just said it was for a Rolling Stones album cover. I was a huge fan, so I was pleased, and also I got paid $100. Not bad for 20 minutes’ work.”

Warhol also photographed Dallesandro’s brother Bobby, and Jackie Curtis, who was another of Warhol’s so-called Superstars.

The shoot took place at 33 Union Square West, which housed Interview’s office and Warhol’s Factory. During the session, a few visitors got an eyeful of rock history.

“There was an architect’s office next door,” O’Brien recalls. “I have my jeans down around my ankles…Andy is kneeling in front of me with his Polaroid, and Fred [Hughes, Warhol’s business manager] is making rude remarks, like, ‘Can’t you make it any bigger?’ The door opens, and these guys walk in in suits, and they’re dumbfounded. And one of them said, ‘Um, this isn’t the architect’s office?’”

Not only did Warhol never tell anyone the identity of the cover model, but O’Brien thinks it’s possible he didn’t even know.

“He probably took these Polaroids, put them on the table, and picked ones he liked. I don’t think it mattered to him [who it was],” says O’Brien. “I don’t know if the fact that I was chosen means I was the best endowed or what.”

As for the jeans pic, O’Brien believes it was Corey Tippin, a makeup artist who was part of the Warhol scene. Tippin didn’t know what the shoot was for, and received $75.

“I knew [Warhol] wanted it to be kind of an erotic photograph. Andy wanted a bulgy crotch,” Tippin says. “[To me,] it had nothing to do with rock ’n’ roll…Those of us in the gay world related to it as a gay iconic image.”

Tippin was also never told the identity of the jeans model on the cover, but is convinced it’s him: “I know my anatomy.”

The cover received some odd tweaks internationally. In Russia, an image of a Soviet Army belt buckle was added to the jeans; in Spain, the jeans photo was replaced by a picture of a woman’s fingers emerging from a can of blood.

Though the “Sticky Fingers” crotch mystery may never be definitively solved, Tippin’s OK with that. “The fact that Andy never authenticated who the model was…I think it’s funny. I think it’s mysterious,” he says. “Though had I known it was for a Stones album cover, I probably would have asked for more than $75.”