He is the Annie Leibovitz of his generation, having shot every culturally relevant celebrity of the past decade — Lady Gaga, Rihanna, Beyoncé. He is the man behind Miley Cyrus’ controversial makeover and directed her video for “Wrecking Ball.” In 2007, he photographed Barack Obama for Vibe. His work appears in nearly every major fashion publication, and he has done campaigns for multibillion-dollar luxury brands.

He also likes to be called ­“Uncle Terry,” has depicted himself copulating with a sheep, and once embarked on a project called “Breaking in the Carpet,” photographing himself ejaculating on rugs in random hotel rooms.

But in the fashion industry, Terry Richardson — he of the plaid shirt, oversized eyeglasses and omnipresent “thumbs-up” gesture — is notorious for years-long, rampant reports of sexually exploiting and abusing his models.

“I was a shy kid,” he has said, “and now I’m this powerful guy with a boner, dominating all these girls.”

Over the past couple of weeks, Richardson, 48, has a new accomplishment. He’s the first photographer of his stature to be the target of an online petition: “Vogue, H&M, Mango, Supreme and all other brands: Stop using ­alleged sex offender Terry Richardson as your photographer.”

The petition is the work of an 18-year-old girl from the outskirts of London named Alice Louise. She has no connection to the fashion industry other than as a consumer. As of Friday, her petition had more than 12,000 signatures.

“You start to question why you see this man everywhere when allegations still exist, and his hardcore pornographic pictures featuring himself, which simulate rape, gagging and choking, are still floating around the Internet,” Louise says. “Potential sexual predators should not be praised in the fashion industry.”

In the past week, H&M announced, via Twitter, that it is reconsidering further collaborations with Richardson: “If these accusations are true, it’s totally unacceptable to us. Currently we’re not working with Terry ­Richardson.”

Equinox also dropped Richardson, who had shot its last three campaigns. “The natural point has now come to explore a fresh direction,” the company said in a statement.

Richardson refused to speak for this story, but released a statement through his publicist.

“The fact that he’s not shooting [Equinox’s] current campaign has nothing to do with the petition,” it read. “As far as any backlash goes, Terry is currently working with a long list of high-profile clients, so we really don’t know what you’re referring to.”

‘I AM A PERVERT’

The first reports of Richardson’s abuse surfaced in 2010, when supermodel Rie Rasmussen told Page Six she’d run into him in Paris.

“I told him, ‘What you do is completely degrading to women. I hope you know you only f–k girls because you have a camera, lots of fashion contacts and get your pictures in Vogue.’ ”

Supermodel Coco Rocha also said she had worked with Richardson once, and was so uncomfortable, she told her agents never again. But Rocha was, by then, powerful enough to make such a demand. Younger models, Rasmussen told Page Six, “are too afraid to say no, because their agency booked them on the job, and [they] are too young to stand up for themselves.”

After Rasmussen’s confrontation, a model named Jamie Peck came forward. She’d modeled for Richardson when she was 19, and wrote that her first shoot with him was fairly tame: “He spoke in the effeminate tones of someone trying very hard not to come off as sexually threatening, despite the fact that he was basically walking around in a hipster ­pedophile costume,” she wrote. He asked her to call him Uncle Terry, and she posed naked while dancing to the Yeah Yeah Yeahs. Then she left.

At the second shoot, Peck said, Richardson asked her to strip; she said she had her period. Then she said, “He asked me to take my tampon out for him to play with,” adding that he’d like to use it to make tea. “I politely declined,” Peck wrote. “It was then that he decided to just get naked.”

According to Peck, Richardson maneuvered her to the couch while he dropped names, told her she should come upstate with him and his famous friends, then “strongly suggested” she give him a handjob while his ­assistants cheered her on. After Richardson climaxed, one of his assistants handed her a towel and she fled, feeling ashamed and “like I needed two showers.”

An aspiring model named Felice Fawn then posted an IM exchange she’d had with a man identifying himself as Richardson, asking if she’d pose for him under certain conditions: “I am a pervert,” he wrote. “Daily 20 models offer me to f–k them for fame.” Fawn declined, and Richardson signed off: “Would have shot you and published you for sure, but no prob.” (Richardson maintains an imposter conducted this exchange.)

In November 2012, Bruce Willis’ and Demi Moore’s daughter Scout tweeted that “last night Terry Richardson tried to finger me. I didn’t let him, obviously. But I did let him photograph me topless in the bathroom.” (Willis later claimed the tweets were fictitious and done for a school project.)

OBJECTS OF LUST

Richardson was born Aug. 14, 1965, in New York City. His father, Bob Richardson, was a well-regarded fashion photographer. He was also bisexual and a bipolar schizophrenic. When Bob was 43, he left Richardson’s mother for then-17-year-old Anjelica Huston, who later said Bob was so abusive, she tried to commit suicide.

When Terry was 9, his mother was in a devastating car accident that left her comatose for a week.

Her recovery was agonizing.

“She was in diapers, couldn’t walk,” Terry said. “It made me very attracted to very dysfunctional, f–ked-up people.”

Richardson dropped out of school in the 10th grade, and by 18 was a heroin addict. He began working with his father on shoots, and struck out on his own after winning an ad campaign for the British designer Katharine Hamnett.

“I sent a bunch of personal pictures — people with their d–ks out and all that — and three days later, they called me and said I had the campaign.”

In 1996, Richardson married model Nikki Uberti, and after she was diagnosed with cancer, left her for model Shalom Harlow.

“I was single,” he has said, “and I was going to explore sexuality.”

When he had his first New York show at Deitch Projects in 2004, some of the gallery’s artists threatened to cut ties in protest.

“Terry was in deep s–t with all those first-year feminist types,” said Vice magazine’s Gavin McInnes. Among Richardson’s subjects: a very young meth- ­addicted prostitute from New Jersey, shot topless, and his own assistant Alex, shot crouched ­under a desk, performing fellatio on Richardson. That show ­became a book, “Terryworld.”

Highly sexual imagery has been commonplace in fashion photography for decades. Helmut Newton and Guy Bourdin mainstreamed a highly ­sophisticated, erotic aesthetic in fashion, but they also worked with women who were clearly of age. Calvin Klein’s ads further pushed boundaries in the ’80s and early ’90s, but there has never been a fashion photographer as prolific, profitable and suspect as Terry Richardson.

He has become the dominant photographer of our time, and it’s a curiously stubborn reign. Setting aside his personal behavior, his technical and artistic work seems emotionally and culturally arrested. If you’re a young, female celebrity — minor or mega — you’ve been shot the same way: against a white back-drop, slightly overlit, barely dressed, and probably putting something into your mouth. From Blake Lively to Kate Upton to Lindsay Lohan to Beyoncé, the treatment’s the same.

It’s the American Apparel aesthetic writ large, on nearly every billboard and magazine cover we see. We’re living in Terry’s world — that of a 12-year-old boy’s ­aspirational sexual fantasies, women nothing more than ­clichéd objects of lust or degradation. His perversion isn’t even original, and it will probably be boredom with his visuals, rather than outrage over his personal behavior, that will mark his ­decline.

In 2010, “Glee” actress Dianna Agron was mortified after a GQ shoot with Richardson. The setup: she and co-star Lea Michele were naughty cheerleaders pursuing a threesome with male castmate Cory Montieth. Agron later apologized to fans who had been made “uncomfortable.”

In 2012, Chloë Sevigny admitted that Richardson’s methods were often manipulative, and that at least she, as a celebrity, was able to enforce boundaries: “[Young models] walk out of there and cry, ‘What did I do?’ ”

COVER STORIES

Very few people will speak on the record about Richardson. Even those rare editors who blackballed him — Kate Betts when she was at Harper’s Bazaar and Dennis Freedman, formerly of W — have never commented.

An anonymous fashion-industry source has said that despite knowing “full well Richardson’s predatory behavior, [he’s] tolerated because industry folk are just sheep. There are only a handful of photographers who have the power, a handful of editors . . . everyone else just follows this small group.”

Even more perplexing: The world of fashion magazines is one of the few industries dominated by women. How they continue to employ a man they’d likely never leave alone with a daughter or friend is a feat of ­rationalization.

It’s also hard to reconcile the complicit endorsement of celebrities whose public images stand in opposition to all Richardson represents: Madonna, who ­recently told Harper’s Bazaar that she’d been raped when she first came to New York, was shot by Richardson for that very issue. Lena Dunham, self-styled feminist of her generation, was shot in her underwear by Richardson for V magazine; Richardson also dates Dunham’s friend Audrey Gelman, the press secretary for comptroller Scott Stringer. (Dunham and Gelman would not comment for this article.) Gloria Steinem posed with Richardson at an event last year, but through a spokesperson said she had no idea who he was at the time.

Since these allegations have surfaced, Richardson has given almost no interviews. In 2012, he told The New York Times that reports of his exploitative behavior were “hurtful.”

Today, Richardson says he is clean and sober. Of shooting girls with “SLUT” written across their foreheads while they give him oral sex or of being jammed into garbage cans while they do the same — Richardson, in 2004, said he was bored of it all. “Lately, I find myself thinking I’d really love to settle down, get married, have kids, have a regular relationship.”

As of Friday, Richardson was still soliciting amateur models on his site: “If you are 18 or older, male or female, and wish to pose nude or topless for an upcoming project, please contact.”