The married senator was the first lady's "true love" and the couple was openly affectionate at family get-aways and social gatherings, according to a new book "Bobby and Jackie: A Love Story."
The book also claims it was Jackie who asked doctors to pull the plug on Bobby after he was shot -- not his wife, Ethel.
"Everybody knew about the affair," Franklin Roosevelt Jr., JFK's undersecretary of commerce, says in the book. "I suspect Bobby would've liked to dump Ethel and marry Jackie, but, of course, that wasn't possible."
Six months after the death of JFK, Bobby and Jackie "exchanged poignant glances" before disappearing together on a May 1964 dinner cruise aboard the presidential yacht the U.S.S. Sequoia and left Ethel upstairs.
"When they returned, they looked as chummy and relaxed as a pair of Cheshire cats," Schlesinger said in the book.
C. David Heymann, the book's author, said he spent two decades researching the work.
Many critics ripped Heymann for basing his allegations on thin evidence.
"It's a new low, and you just wonder how far people are willing to go," Laurence Learner, author of "The Kennedy Men," "The Kennedy Women," and "Sons of Camelot" told The New York Daily News last month.
"[Heymann] is just trying to make a buck. Yes, Bobby and Jackie had a relationship as friends, but [the romance] is a total exaggeration. I feel sorry for Heymann," he said.
The book also claims Jackie had a tryst with actor Marlon Brando, who wanted to expose the secret affair to the world before he ultimately edited it out of his memoir.
"I'm not sure she knew what she was doing sexually, but she did it well," Brando reportedly wrote in his unpublished work.