In an exclusive story penned for VanityFair.com, Johnson -- most notable for being the first black model to ever appear on the cover of American Vogue in 1974 -- writes for the first time about her alleged experience being drugged by Bill Cosby in 1986.
Johnson, now 62, says she first came into contact with Cosby when an agent told her that the comedian wanted her to audition for a role on The Cosby Show. She says she went to a taping of the show, and then talked with him in his office afterwards about the troubles she had in her previous marriage, and where she wanted to go in her career moving forward. After going to a second taping -- this time with her daughter in tow -- the two got a tour of Cosby's New York Brownstone.
"Looking back, that first invite from Cosby to his home seems like part of a perfectly laid out plan, a way to make me feel secure with him at all times," she says. "It worked like a charm."
Johnson says she came back to Cosby's house a few days later to read for the Cosby Show part they initially discussed, during which he wanted her to "pretend to be drunk" to see how she handled various scenes. She alleges that he insisted she drink a cappuccino from his espresso machine, even when she initially refused.
She alleges that he drugged her though the coffee drink.
"Now let me explain this: I was a top model during the 70s, a period when drugs flowed at parties and photo shoots like bottled water at a health spa," she discloses. "I'd had my fun and experimented with my fair share of mood enhancers. I knew by the second sip of the drink Cosby had given me that I'd been drugged -- and drugged good."
"My head became woozy, my speech became slurred, and the room began to spin nonstop," she alleges. "He put his hands around my waist, and I managed to put my hand on his shoulder in order to steady myself. As I felt my body go completely limp, my brain switched into automatic-survival mode. That meant making sure Cosby understood that I knew exactly what was happening at that very moment."
She lashed out by telling him, "You are a motherf*cker aren't you?"
Johnson says that after repeatedly calling Cosby a "motherf*cker," he became so angry that he dragged her down the stairs and shoved her into a taxi cab.
"The next day I woke up in my own bed after falling into a deep sleep that lasted most of the day," she says. "I had no memory of how I got into my apartment or into my bed, though most likely my doorman helped me out. I sat in there still stunned by what happened the night before, confused and devastated by the idea that someone I admired so much had tried to take advantage of me, and used drugs to do so. Had I done something to encourage his actions?"
Deciding to confront Cosby shortly about the incident, she says she dialed the private number he gave her, but was shocked when his wife Camille picked up. She claims Camille told her it was "very late" -- 11 p.m. -- and that the two were in bed together.
Johnson says she never called back.
"At a certain moment it became clear that I would be fighting a losing battle with a powerful man so callous he not only drugged me, but he also gave me the number to the bedroom he shared with his wife," she explains. "How could I fight someone that boldly arrogant and out of touch? In the end, just like the other women, I had too much to lose to go after Bill Cosby. I had a career that would no doubt take a huge hit if I went public with my story and I certainly couldn't afford that after my costly divorce and ongoing court fees."
About her decision to previously stay silent as more women began to come forward with sexual assault allegations against Cosby, she says the "plight of the black male" -- referencing the recent headline-making cases of Trayvon Martin, Michael Brown and Eric Garner -- made her hesitant to tell her story.
"Over the years I've met other women who also claim to have been violated by Cosby," she says. "Many are still afraid to speak up. I couldn't sit back and watch the other women be vilified and shamed for something I knew was true."
"Finally, I reached the conclusion that the current attack on African American men has absolutely nothing to do at all with Bill Cosby," she adds. "He brought this on himself when he decided he had the right to have his way with who knows how many women over the last four decades."
Her fellow supermodel Janice Dickinson -- who Johnson calls a "longtime friend" in her VanityFair.com piece -- talked to ET in November, when she claimed that she was sexually assaulted by Cosby in 1982.