The former England captain's five-year contract with the Major League Soccer side expired last month and he had been linked with various clubs, including former club Manchester United and their Premier League rivals Tottenham, before signing a new two-year deal in California.
He said: "I was offered the chance (to return to the Premier League), yes, but I'm happy here so that was a major factor in my decision - my family, my children, and playing for the Galaxy. That was what I was passionate about."
Asked which clubs had made him offers, Beckham said coyly: "One or two."
Despite his advancing years, Beckham insists he is far from finished.
"Retirement was never a part of my plans," he said at a Galaxy news conference.
"It had been talked about by other people but it always is, when you get to this stage in your career.
"I've not even started thinking about retirement yet.
"Last season was such a special season, not just because we were champions but the way we played and conducted ourselves on and off the field.
"I could feel a change within the players."