He helped kill the pope — so his pals could stay out of hell.

That’s the shocking claim from longtime Colombo gangster Anthony Raimondi, who says that, in 1978, he went to Italy with a team of hit men who whacked John Paul I. They allegedly poisoned him with cyanide just 33 days into the pontiff’s reign, according to Raimondi’s new book, “When the Bullet Hits the Bone,” out now from Page Publishing.

Raimondi, the nephew of legendary godfather Lucky Luciano, claims he was recruited for the murder at the age of 28 by his cardinal cousin, Paul Marcinkus, who ran the Vatican bank. Raimondi’s job was to learn the pope’s habits and be on hand to observe as Marcinkus knocked out John Paul by spiking his nightly cup of tea with Valium.

“I stood in the hallway outside the pope’s quarters when the tea was served,” he writes, adding that the drug did its job so well that their victim wouldn’t have stirred “even if there had been an earthquake,” he recounts. “I’d done a lot of things in my time, but I didn’t want to be there in the room when they killed the pope. I knew that would buy me a one-way ticket to hell.”

Instead, he stood outside the room as his cousin readied a dose of cyanide, he claims. “He measured it in the dropper, put the dropper in the pope’s mouth and squeezed,” Raimondi writes. “When it was done, he closed the door behind him and walked away.”

After the snoozing pontiff was force-fed the poison, a papal assistant checked on him, then cried out that “the pope was dying” — after which Marcinkus and two other cardinals in on the plot “rushed into the bedroom like it was a big surprise,” Raimondi writes. A Vatican doctor was summoned, who ruled that John Paul I had suffered a fatal heart attack, he writes.

They used Valium and the deadly toxin so as to kill the pope painlessly — and to curry favor in the afterlife, Raimondi claims. To prove John Paul I didn’t suffer, Marcinkus and cohorts Pietro Palazzini and Antonio Ribeiro, also his cousins, needed Raimondi to testify on their behalf before God, he claims. “They said when we die I would be their witness,” Raimondi, now 69, told The Post.

They targeted the pope because he had threatened to expose a massive stock fraud run by Vatican insiders, according to the book.

The billion-dollar scam involved a forgery expert at the Vatican who faked the church’s holdings in blue-chip American companies such as IBM, Sunoco and Coca-Cola. Mobsters then allegedly sold the phony stock certificates to unsuspecting buyers.

John Paul I had vowed to defrock the perpetrators, which included Marcinkus and about “half the cardinals and bishops in the Vatican,” Raimondi told The Post. “They would have been thrown out and subject to the laws of the US and Italy,” he said. “They would have gone to jail.”

Had John Paul I “kept his mouth shut,” Raimondi writes, “he could have had a nice long reign.”

The body was barely cold when a new plan was conceived to kill his successor, John Paul II, who appeared poised to take action against the scammers as well, Raimondi writes. So the made mob man was summoned back to the Vatican and told to prepare for a second murder.

“ ‘This guy’s gotta go, too,’ they said. ‘No way,’ I said. ‘What are you going to do? Just keep killing popes?’ ”

Ultimately, John Paul II decided not to act because he knew he too would die, Raimondi told The Post, then went on to become the second-longest-serving pontiff in modern history, until his death at 84 in 2005.

His change of heart also prompted a booze-fueled celebration among crooked cardinals and mobsters in Vatican City, according to Raimondi.

“We stayed and partied for a week with cardinals wearing civilian clothes, and lots of girls,” he writes. “If I had to live the rest of my life in Vatican City, it would have been OK with me. It was some setup. My cousins all drove Cadillacs. I am in the wrong business, I thought. I should have become a cardinal.”

Those who dismiss his claims, or point to the fact his story resembles the plot from “The Godfather III,” Raimondi shrugs. “It was a terrible movie. To tell you the truth I don’t really remember it. What I said in the book I stand by till the day I die. If they take [the pope’s body] and do any type of testing, they will still find traces of the poison in his system.”

Raimondi’s book is loaded with other over-the-top revelations, including intimate details on the Lufthansa heist, one of the most notable rip-offs in mob lore.

But his take differs from the movie “Goodfellas,” and the book “Wiseguy” on which it was based, as both featured James “Jimmy the Gent” Burke, played by Robert De Niro, and Ray Liotta’s Henry Hill as the brains behind the epic theft.

Raimondi — a fixer and earner for the Colombos — claims Lufthansa’s real mastermind was Jewish mobster Meyer Lansky, head of the Kosher Nostra and a mentor of Raimondi’s, he claims. “I first brought him in on the plan during a trip to his home in Miami,” he writes.

Another one of Raimondi’s cousins was friends with gangster Burke, who allegedly got a tip about big money coming through JFK Airport.

But when the information circulated among the Lucchese hierarchy, the family couldn’t “figure out how to put this deal together,” Raimondi writes, so he convinced Lansky to come to New York and orchestrate the smash-and-grab job.

“Everything was so well planned,” he writes. “Meyer had set the time for everything to happen. He had it mapped out so everybody had a precise job they had to do.”

In the end, Raimondi claims, the gang got away with far more money than previously believed: about $45 million, including cash, jewelry and $35 million in bearer bonds that Lansky believed had been stolen before being shipped to New York, says the book.

Raimondi hid the bonds at his father’s house, after which Meyer fenced them at “85 cents on the dollar,” he writes, and the loot got spread around all five organized-crime families at a social club in Brooklyn on Cortelyou Road.

“We were there for hours, counting the money and giving everybody their end,” Raimondi writes. “The bosses came down from all the families personally . . . They were getting millions.”

Everyone was warned to keep low profiles and not make extravagant purchases. But several didn’t — and were systematically rubbed out, Raimondi writes.

Michael Vecchione, a former top prosecutor at the Brooklyn DA’s office who went after Colombo mobsters and has written three books on crime-fighting, is dubious. “I do remember the name Raimondi coming up, but I never heard anything about Meyer Lansky being involved in the Lufthansa heist,” he said. “But there’s no way to verify what this guy is saying.”

As for the author, he claims he managed to avoid prosecution for years, because he and his crew paid millions of dollars from his own loansharking and clubs to Mayor Ed Koch, with Koch aide Bess Myerson acting as bag lady.

“We had illegal casinos, shylock money, and Koch got a piece of everything and we never had a problem with the law,” he writes. “I’d take the package for Bess and bring it to [a friend’s] house, where she would come and collect it. I’d put it in a regular canvas bag, and she would just put it in her briefcase.”

Raimondi, a hulking and fiercely loyal Colombo member nicknamed Pluto, has a fascinating personal story as well, as he had regular contact with notable gangland figures such as Carmine Galante, Allie Boy Persico and Joe Colombo.

He alleges he dodged life in federal prison for a murder he committed as a teen in Brooklyn after the Army recruited him to become a sniper during the Vietnam War.

His job, Raimondi claims, was to drop in behind enemy lines in Cambodia and assassinate North Vietnamese fighters, which he says he did ruthlessly.

He allegedly returned to the US with a clean record and threw himself into mob business, benefitting from the help of Lansky, who, Raimondi writes, “taught me so many different ways of shaking down a guy. He also taught me so many ways to kill a guy, because Meyer was deadly. Don’t let nobody fool you: Meyer killed a lot of men in his time.”

Raimondi, who is now fighting cancer and living in Brooklyn, said he decided to quit the life and tell his story because “I don’t need this s–t any more.”

“All the old guys either went to prison or they died or went into witness protection,” he told The Post.

“The new guys didn’t do things the old way. I said, you know what, time to leave.”