In her first television interview, Alford described her relationship with the president as "exciting," "glamorous," and "fun."
Her bombshell revelations include claims that, on Kennedy's request, she performed oral sex on Dave Powers, one of the president's top aides, while he watched.
"The president swam over and whispered in my ear, 'Mr. Powers looks a little tense, would you take care of it?' It was a dare but I know exactly what he meant ... it was pathetic," she said, reading from her book.
Alford told Vieira that the affair, which was consensual, began in 1962 when Powers asked her to join the president at a party to welcome a new staffer. Afterwards, she said he gave her a private tour of the quarters, at the end of which they had sex in Jackie Kennedy's bedroom. It was the first time she'd had sex with anyone, she explained.
"I wouldn’t describe what happened that night as making love, but I wouldn’t call it nonconsensual either," she said, adding that she was "overpowered in the sense that he was the president ... I don't consider it was rape."
The encounter was the beginning of an 18-month long relationship, Alford said. She said she would spend nights with him at the White House's private residence, as well on official trips where she would wait for him in a hotel room until he summoned her. He gave her gifts and even called her while she was away at college.
Looking back, she said that it was an "imbalanced" relationship for a 19-year-old to have. However, she said that "I still wouldn't say no" and she "wasn't really in the wrong." She recalled fond memories of her time with the president.
"He had a collection of little yellow rubber ducks and they were in the bathtub and rubber ducks sort of became part of the game," she said. "We had races with rubber ducks in the bathtub."
Not of all her memories were so pleasant.
"It wasn't a romantic affair," she admitted. "I don't ever remember him kissing me."
At one point, she said she thought she was pregnant and told Powers, who told her he could arrange for her to have an abortion.
"He said he would put me in a touch with someone who would put me in touch with someone who would put me in touch with someone if I should need help," she said.
Though he was married, she said she "didn't feel guilty" about the affair and believed the president cared about her.
"I'm not going to say he loved me, but I think he did like me a lot," she said. "Just the way he was, the way he smiled with me. I feel that he did. I feel that he actually cared about me."
She also said she was relieved to be finally speaking out on her experience.
"When you keep a secret, and when you keep silent about something, you do it because you think it's keeping you safe, but in fact, it's deadly," she said.
Alford's book, "Once Upon a Secret: My Affair with President John F. Kennedy and Its Aftermath," was released on Monday.
Watch more from the interview on "Rock Center":