After weeks of negotiations with PSG, the 36-year-old midfielder and former England captain decided he doesn't want to move his family from the United States.
"David Beckham is not coming," PSG President Nasser al-Khelaifi said at the Qatar Open tennis tournament. "We feel a little disappointed. But both sides agreed it would be better that we not do the deal ... maybe in the future."
Beckham's five-year contract with the Galaxy ended after he won his first MLS Cup in November. He was wooed by several clubs across Europe.
"David Beckham is (with) Los Angeles," al-Khelaifi said. "And he's going to stay there."
Beckham will try to finalize a new, improved rolling one-year contract this week with the Galaxy, which was paying him an annual base salary of $6.5 million.
French media had reported that Beckham would have been paid almost double that at PSG, whose Qatari owners have spent more than $100 million on players during six months in charge.
Beckham and wife Victoria, a former member of the "Spice Girls," moved to California in 2007 after four years at Real Madrid.
The celebrity couple now have four children and decided during a Christmas break in England that they did not want to move back to Europe permanently.
"I'm very proud of the time that I've spent with the Galaxy and it might continue," Beckham stressed recently.
The Galaxy's recent success and the signing of Ireland captain Robbie Keane have shown Beckham that the LA club can meet his ambitions during the final years of his career, which began at Manchester United.
Beckham is also a regular starter with the Galaxy, whose new season begins in March. He has expressed hope of playing for Britain's football team at the London Olympics as one of three players above the age of 23.
AP Sports Writer Rob Harris in London contributed to this report.