Inga Arvad was John F. Kennedy’s great love — “Inga Binga,” the one woman with whom he could be himself, according to many who knew him.

But when Arvad was working in Berlin as a journalist in the mid-1930s, Adolf Hitler found her so fascinating that he invited her to the 1936 Berlin Summer Olympics, even hosting a lunch in her honor.

They weren’t the only ones charmed by her. When Arvad worked in Hollywood as a gossip columnist, male actors regularly declared her more beautiful than some of their leading ladies.

Even FBI director J. Edgar Hoover was obsessed with Arvad, albeit for other reasons. Convinced the blonde was a Nazi spy who had infiltrated the highest ranks of American government through her job as a columnist for the Washington Times-Herald, he had her investigated for years.

“There was a notion that beautiful exotic women who speak a lot of languages were inherently suspicious,” says Scott Farris, author of the new book “Inga” (Lyons Press), noting that Arvad’s FBI file was 1,200 pages long.

“As it turns out, Nazi Germany actually had a terrible espionage network,” he adds. “But the FBI didn’t know that at the time. They were desperate to find something. And the less they found, the more they were convinced [Arvad] was hiding stuff.”

She was innocent. But Arvad didn’t always help her own cause.

Born in 1913 in Denmark, and raised by her mother to be the perfect woman, Arvad was crowned Miss Denmark 1931 before moving to New York to attend the Columbia School of Journalism.

While reporting in Berlin, she had penned flattering profiles of top Nazi officials, including Hitler, of whom she wrote, “You immediately like him . . . The eyes, showing a kind heart, stare right at you. They sparkle with force.”

To be fair, Farris points out that this is not quite as outrageous as it sounds, as it was the mid-’30s. “A lot of people were fascinated by Hitler in 1936,” he says. “No one could envision the Holocaust at this point.” Hitler even gave Arvad an autographed picture of himself, signed, “To Inga Arvad, in friendly memory.”

She scooped the continent with the news of Nazi leader Hermann Göring’s engagement to actress Emmy Sonnemann. “Never has the bride looked more enchanting,” Arvade wrote of the wedding, describing how Sonnemann’s arm extended in a Nazi salute.

The Nazis enjoyed her profiles so much, in fact, that they asked her to become a spy for them, something Arvad said she would consider. Instead, it was her wake-up call. She took the next plane to Copenhagen, Denmark, stunned and scared.

She later moved to Washington, DC, where she and Jack Kennedy, then a 24-year-old naval ensign, were introduced in November 1941 by his sister Kick, a close friend of Arvad’s. She was still wed — her second marriage, following a brief teenage union — to Hungarian film director Paul Fejos at the time.

Initially, Kennedy’s controlling father, Joseph, had no issues with the relationship, assuming it to be short-lived and primarily sexual. While the latter was true — “[Jack’s] got a lot to learn and I’ll be happy to teach him,” Arvad said — the dalliance quickly became serious.

“Within a few weeks, Inga understood Jack, as Jack himself would later note, better than most of his family and long-time friends,” writes Farris.

For a while, the pair entertained the idea of marriage, with Kennedy even visiting a priest to inquire about Arvad converting to Catholicism and having her first two unions annulled.

But a future was not in the cards for a twice-married Protestant and the aspiring politician from America’s most ambitious Catholic clan. Eventually, Joseph Kennedy would have his way.

“They talked about getting a ranch [out] West, and he’d teach at a college,” says Ferris. “And then [Jack] realized . . . Joe had the leverage to break up the relationship. You have these two remarkable people, with all the charm and charisma in the world — they have everything in the world except the one thing they want, which is each other.”

The relationship ended in 1942. “You have two backbones,” Arvad wrote JFK in a letter. “Your own and your father’s.”

Arvad, who’d divorced Pejos in 1942, wed actor Tim McCoy in 1946. She became a US citizen, had two sons and raised them in La Cañada, California.

Kennedy would go on to marry Jacqueline Bouvier in 1953. After he became president, Arvad sent him a telegram of congratulations — but never heard back.

When Kennedy was assassinated in November 1963, Farris writes, Arvad “silently rose up from her chair, went into her bedroom, and shut the door. She stayed there and cried for hours.”

Shortly after the assassination, Kennedy friend Arthur Krock, with whom Arvad had stayed in touch, sent her a condolence letter, mimicking Kennedy’s Boston accent: “Every time I saw President Kennedy he would say to me with a twinkle in his eye, ‘How’s Inger?’ ”