This comes after the National Enquirer published erotic text messages sent between him and his mistress Lauren Sanchez last month. Since then, private investigators for the billionaire have been looking into how the Enquirer got the texts.
Instead, he published what he said were emails from Enquirer executives to a lawyer representing de Becker.
According to the letters, in exchange for not publishing these photos, AMI's Deputy General Counsel, Jon Fine, wanted Bezos and his team to acknowledge that "they have no knowledge or basis for suggesting that AMI's coverage was politically motivated or influenced by political forces, and an agreement that they will cease referring to such a possibility".
Bezos went on to say that, "Any personal embarrassment AMI could cause me takes a back seat because there's a much more important matter involved here", Bezos wrote. He added, "It would give no editor pleasure to send this email".
The Amazon boss didn't try to hide the potential for embarrassment, writing "of course I don't want personal photos published" and noting what he called "AMI's long-earned reputation for weaponising journalistic privileges".
"If in my position I can't stand up to this kind of extortion", he wrote, "how many people can?"
Their announcement came just before the National Enquirer carried reports about the tech titan's extramarital affair. Bezos began to investigate how the leak of his private information came about.
AMI recently admitted it had co-ordinated with the Trump presidential campaign to pay a Playboy model $150,000 (£115,000) in hush money to keep quiet about her alleged affair with Mr Trump. The company has been cooperating with investigators in the Southern District of NY ever since it admitted to making a $150,000 "catch-and-kill" payment to rid of a story about an alleged affair Trump had with former Playboy model Karen McDougal. De Becker proceeded to tell media that the leak was politically motivated. 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.
"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". In the next sentence, Bezos describes the non-prosecution agreement struck in September between AMI and the Justice Department.
Frozen cat thawed out after being found unresponsive in Montana snow bank
They used warm water, hair dryers, heated towels, and a heated kennel to get her body temperature back to normal. Fluffy's owners said she is now strictly an indoor cat. "And then they realised "oh my gosh, she's not moving".
American Media Inc (AMI), the owner of the National Enquirer, did not immediately return a request for comment. The deal not to prosecute was conditional on AMI not committing another crime, the office said. "For prosecutors, your worst nightmare is watching a cooperation deal unravel".
Representatives of AMI had no immediate comment on Thursday.
The alleged blackmail attempt was in connection with pictures of Bezos with former TV host Lauren Sanchez.
Hours later, the first Enquirer story on his relationship with Sanchez posted online. Bezos contends that his own investigation displeased the Enquirer brass. It also said the photos were newsworthy, given Bezos' prominence.
This whole story, as Bezos would put it, is complexifying my brain. He also published correspondence between AMI and lawyers for his investigator, Gavin de Becker. Bezos said in his post. "It's ripped right out of the law books".
Sounds like soon some people at The National Enquirer are going to "learn to code".
But the company has admitted in the past that it engaged in what's known as "catch-and-kill" practices to help Trump become president.
· Mr. Bezos face selfie at what appears to be a business meeting.