He also wrote in "True Compass" that he accepted the conclusion that a lone gunman assassinated his brother President John F. Kennedy.
The memoir is to be published Sept. 14 by Twelve, a division of the Hachette book group. The 532-page book was obtained early by The New York Times and the New York Daily News.
In it, Kennedy said his actions on Chappaquiddick Island on July 18, 1969, were "inexcusable." He said he was afraid and "made terrible decisions" and had to live with the guilt for more than four decades.
Kennedy drove off a bridge into a pond. He swam to safety, leaving Kopechne in the car.
Kopechne, a worker with slain Sen. Robert F. Kennedy's campaign, was found dead in the submerged car's back seat 10 hours later.
Kennedy, then 37, pleaded guilty to leaving the scene of an accident and got a suspended sentence and probation.
He wrote that he had no romantic relationship with Kopechne, and he hardly knew her. He said they were both getting emotional about his brother's death and decided to leave the party that was hosted by Robert Kennedy's former staffers.
Kennedy also wrote in the memoir that he always accepted the official findings on his brother John's assassination.
He said he had a full briefing by Earl Warren, the chief justice on the commission that investigated the Nov. 22, 1963, Dallas shooting, which was attributed to Lee Harvey Oswald. He said he was convinced the Warren Commission got it right and he was "satisfied then, and satisfied now."
In the book, Kennedy wrote candidly about his battle with brain cancer and his "self-destructive drinking," especially after the 1968 death of his brother Robert.
After his brothers' assassinations, Kennedy said he was easily startled at loud sounds, and would hit the deck whenever a car backfired.
He expressed regret over getting drinks with nephew William K. Smith in Palm Beach in 1991, after which Smith was charged with rape. He was later acquitted.
He also explained why he decided to run for the presidency in 1980, saying he was motivated in part by his differences with then-President Jimmy Carter. He criticized Carter's go-slow approach to providing universal health care.
As a 9-year-old boy at the Riverdale Country School in New York, Kennedy said he would hide under his bed, petrified of a dorm master he thought was sexually abusive.
The book was written with the help of a collaborator and was based on contemporaneous notes taken by Kennedy throughout his life and hours of recordings for an oral history project.
Kennedy died last week at age 77.