He claims he was recruited for the murder at the age of 28 by his cardinal cousin, Paul Marcinkus, who ran the Vatican bank.
Raimondi was tasked with learning all of the pope's habits and be on hand to observe as Marcinkus knocked out John Paul by spiking his 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".
"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 chose to stand outside the room as his cousin prepared a dose of cyanide.
"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 pope was force-fed the poison, one of his assistants checked in on him, then cried out that "the pope was dying".
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 and ruled that John Paul I had suffered a fatal heart attack.
They chose Valium and cyanide to kill the pope painlessly - hoping to curry favour in the afterlife.
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.