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.
However, the 36-year-old, who was also pursued by Paris Saint-Germain, has now signed a new two-year deal with the Galaxy, with whom he won the 2011 MLS Cup.
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 Thursday's 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."
Beckham will now begin pre-season preparations ahead of the new MLS season, but the Englishman also has a return to the United Kingdom on his radar, with Great Britain fielding a team in the London Olympics this summer.
Asked about his dream of captaining the British team, Beckham said: "Obviously I've had conversations with Stuart Pearce, but as for being captain, it hasn't even been decided if I will be selected.
"As long as I'm fit, healthy and in form, then hopefully I'll have a chance of making the team.
"I'd love to be captain. I've been captain a few times for my country before and to lead them into an Olympics would be special for any player."
Beckham's priority for the time being, however, is his crusade to raise the profile of the sport across the Atlantic.
"For me, soccer's the number one sport around the world, apart from America," he said.
"I want to get soccer to another level in the US. I've felt a change in the last two years and don't want to walk away from it - I want to continue to be a part of that growth."