Gavin De Becker launched an investigation after the National Enquirer published intimate texts that Mr Bezos had sent to his mistress, television anchor Lauren Sanchez.
Shortly before their publication, Mr Bezos had become the subject of tabloid stories after the announcement of his divorce to wife MacKenzie on Twitter.
Last month, Mr Bezos accused the newspaper’s owner of trying to blackmail him with the threat of publishing “intimate photos” he allegedly sent to Ms Sanchez unless he did not publicly state that the tabloid’s coverage of him was not politically motivated.
After the investigation, Mr De Becker concluded “with high confidence that the Saudis had access to Bezos’ phone and gained private information.”
In an article for The Daily Beast website, Mr De Becker said the parent company of the National Enquirer, American Media Inc, had privately demanded that he deny finding any evidence of “electronic eavesdropping or hacking in their newsgathering process.”
He added: “As of today, it is unclear to what degree, if any, AMI was aware of the details.”
Mr De Becker alleged that the Saudi government has targeted the Washington Post, which Mr Bezos purchased in 2013, following the death of one of its columnists, Saudi national Jamal Khashoggi.
Mr Khashoggi, who was sharply critical of Saudi’s crown prince Mohammad bin Salman, was killed in the Saudi consulate in Istanbul in October.
“Some Americans will be surprised to learn that the Saudi government has been very intent on harming Jeff Bezos since last October, when the Post began its relentless coverage of Khashoggi’s murder,” Mr De Becker wrote.
A spokesman for the Saudi embassy in Washington did not immediately return a request for comment.
In February, the kingdom’s minister of state for foreign affairs said Saudi Arabia had “absolutely nothing to do” with the National Enquirer’s reporting on Jeff Bezos.
AMI also did not immediately respond to a request for comment but has previously said that it acted lawfully in the reporting on the affair.
Mr De Becker said he has turned over the findings of his investigation to US federal officials.