"Rather than capitulate to extortion and blackmail, I've chose to publish exactly what they sent me, despite the personal cost and embarrassment they threaten", Bezos wrote in the post, which was entitled "No thank you, Mr. Pecker" and included copies of emails from AMI.
Bezos revealed in the post, published on Medium, what he said was the full text of emails his representatives got from executives with AMI, the publisher of the National Enquirer. In exchange for a promise to not publish embarrassing photos obtained from his text messages, AMI's general counsel Jon Fine asked for Bezos and his lawyer for a statement "affirming that they have no knowledge or basis for suggesting that AM's coverage was politically motivated or influenced by political forces".
In a lengthy blog post published on Thursday, Mr Bezos made several claims about the National Enquirer and its parent company, American Media Inc (AMI).
A spokesman and an attorney for AMI did not immediately respond to messages seeking comment. AMI and its owner, David Pecker, have been accused of buying salacious stories about Donald Trump and killing them so they can't harm the president.
In its January 9 story, the Enquirer reported that Bezos sent "sleazy text messages and gushing love notes" to Sanchez, months before Bezos announced he was splitting up with his wife, MacKenzie.
In an extraordinarily personal online post, Mr Bezos said intermediaries of Mr David Pecker, chairman of American Media Inc (AMI), the owner of The Enquirer, had approached him to stop his investigation.
Bezos' letter to the media company was published Thursday on Medium.com.
Plan to evacuate royals in case no-deal Brexit sparks riots
Irish finance minister Paschal Donohoe said on Tuesday that there was "no such thing" as a "managed no-deal Brexit". But May's spokesman, James Slack, denied that the Brexit process was deadlocked.
Robert Mintz, a former federal prosecutor now in private practice, said Bezos' allegations, if accurate, could have serious consequences for both prosecutors and AMI. "I prefer to stand up, roll this log over, and see what crawls out".
Patrick Whitesell and Lauren Sanchez at the Los Angeles Premiere Of Warner Bros.
Bezos mentions Trump in his post, by the way.
In one e-mail that Mr Bezos disclosed, Mr Howard wrote that The Enquirer had obtained photos of Mr Bezos and Ms Sanchez as part of its "news-gathering". In 2010 the Enquirer began running articles that encouraged the idea of a Trump presidential campaign, according to the Associated Press.
Bezos usually stays out of the public eye, frequently delegating announcements and public Amazon business updates to his executives.
Bezos, his newspaper and Amazon are all regular targets of Trump's signature Twitter tirades.
His blog contained itemised details of 10 pictures in an email from the magazine's editor Dylan Howard, who said they had been "obtained during our newsgathering".
He added that any personal embarrassment from the revelations took "a back seat because there's a much more important matter involved here".