It is based on a draft of his never-before-published memoir. The former boxer and Garland manager died in 2005.
Their affair began in 1951, while she was still married to director Vincente Minnelli, Luft wrote.
See photos of the couple together:
Sid Luft and Judy Garland together
Sid Luft and Judy Garland together
(Original Caption) Singing star Judy Garland who recently announced she'd make her permanent home in England, but according to rumor has changed her mind, and will live in New York, is shown at the Harwyn here, with her husband Sid Luft.
(Original Caption) Screen star Judy Garland gets an affectionate kiss on top of the head, and an orchid from husband Sid Luft, as she arrived in London from Paris here. Judy, who had just completed the film A Star Is Born, had been vacationing on the Rivera and in Paris with her husband. Luft arrived in London a few days before she did. They left the vacationing spots for the United States the day before this photograph.
(Original Caption) Actress Judy Garland an and husband Sid Luft appeared in court here when actress Lynn Bari brought Charles against Luft, her former husband on $3,627 in unpaid alimony for 1952. Miss Bari stated that Luft had agreed to pay her 10 percent of his income but Attorney S. S. Luft was hiding his true income as Agent for Miss Garland by filing two different income tax returns, one for the Government and the other showing losses for his first wife.
(Original Caption) Judy Garland and her manager and boyfriend, Sid Luft, don't look too ill at ease, as they are pictured in Los Angeles Superior Court on Thursday, minutes after an order for Miss Garland's arrest was issued by Judge Louis Burke. She was to testify as a witness in a suit brought by Luft's former wife, actress Lynn Bari.
(Original Caption) After completing her latest movie, A Star Is Born, Judy Garland takes it easy at Monte Carlo, as she and her husband Sid Luft and Movie Executive jack Warner, (R), attend a benefit performance for French polio victims. Glamorous Marlene Dietrich was the headliner at the show.
(Original Caption) Vivacious Judy Garland smiles back over her shoulder at an applauding coterie of her fans, as she leaves the premiere of her latest film, A Star is Born with her husband Sid Luft. the film Judy's first in several years, was acclaimed by a celebrity packed audience.
(Original Caption) Judy Garland, daughter Liza, 7, and Judy's husband, Sid Luft, are shown as they arrived on the 20th Century from the West Coast this morning. They are here to attend the formal New York premiere of Warner Brothers A Star is Born, in which Judy stars with James Mason.
(Original Caption) Judy Garland and her manager husband, Sid Luft, are playing with Liza, 10, Judy's daughter by her second marriage, in their Plaza Hotel Suite. Judy was returning to the palace, where she scored some of her greatest triumphs to climax her great comeback. After her New York engagements, Judy was scheduled to take her show to London.
(GERMANY OUT) Garland, Judy *1922-1969+Sï¿½gerin, Schauspielerin; USAmit Ehemann Sid Luft und den Kindern Joe und Lorna- 1957 (Photo by ullstein bild/ullstein bild via Getty Images)
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He was acting as her manager at the time for her show at New York's Palace Theater. He recalled that he wasn't overly enthusiastic.
"I found myself saying, 'Of course I want your baby, but we've got a show to do," he wrote.
"Because of my negative reaction, Judy didn't confide in me where and when she was going to have the abortion. I wasn't attentive. I didn't send flowers," he said, according to an excerpt of the book published in People magazine.
They later married, and were husband-and-wife from 1952 to 1965.
He is credited with reviving her career in the 1950s after MGM canceled her contract. He produced her 1954 comeback film, "A Star is Born," which earned her an Academy Award nomination for best actress.