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 St 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 (GB coach), 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."
David Beckham Factfile
1975: Born Leytonstone, May 2.
1991: Joins Manchester United as trainee.
1992: Makes debut against Brighton in the League Cup on September 23. Wins FA Youth Cup.
1993: Signs professional contract at Old Trafford.
1995: Joins Preston on loan in February and scores two goals in five games.
1996: Helps United to Premier League and FA Cup double.
Scores goal of the season on opening day at Wimbledon, lobbing Neil Sullivan from the halfway line. Makes his England debut in the 3-0 win in Moldova.
1997: Collects another championship winners' medal, voted PFA Young Player of the Year.
1998: Scores first England goal, a free-kick against Colombia in Lens on June 26. Sent off in second-round penalty shoot-out defeat against Argentina.
1999: Helps United win the Premier League, FA Cup and, memorably, the European Cup after coming from behind to beat Bayern Munich with two late goals.
Runner-up in World Player of the Year awards, behind Rivaldo.
2000: May - Collects fourth championship winner`s medal as United win title by a record 18 points.
November - Named England captain for the November friendly with Italy in Turin by stand-in boss Peter Taylor.
2001: May - Collects another Premier League title with United.
October - Curls in a 25-yard last-minute free-kick against Greece at Old Trafford to earn England a 2-2 draw and send them into World Cup finals.
December 9 - Voted BBC Sports Personality of the Year.
2002: May 11 - Signs new three-year contract reported to be worth between £90,000 and £100,000 a week.
June 7 - Scores from the penalty spot in the World Cup group stage match against Argentina to seal a 1-0 win.
England bow out in the quarter-finals at the hands of eventual winners Brazil.
2003: February - Manchester United boss Sir Alex Ferguson accidentally kicks a boot into Beckham's face in frustration at United's FA Cup defeat to Arsenal.
June 14 - Awarded an OBE in the Queen's Birthday Honours for services to football.
June 17 - United announce they have accepted a £25million bid from Real Madrid for Beckham, who agrees personal terms.
July 1 - Passes medical with Madrid and signs four-year deal.
2004: June 24 - Misses a penalty as England lose to Portugal in a shoot-out in the Euro 2004 quarter-finals in Lisbon.
2005 - November: Captains England for 50th time in friendly against Argentina in Geneva.
July 2 - Stands down as England captain.
August 11 - Dropped from squad for friendly against Greece, Steve McClaren's first match as manager.
2007: January 11 - Beckham announces he will leave Real Madrid and join Major League Soccer club Los Angeles Galaxy on a five-year contract in August.
January 13 - Real Madrid coach Fabio Capello says Beckham will never play for the club again.
May 26 - McClaren hands Beckham a shock England recall for matches against Brazil and Estonia.
June - Wins the La Liga title with Madrid, having won back his place in the team.
August 16 - Beckham scores his first goal for Galaxy on his full debut in the SuperLiga semi-final meeting with DC United with a trademark free-kick.
2008: January 31 - Left out of Capello's first England squad for friendly against Switzerland.
March 26 - Wins 100th cap in the friendly against France.
October 30 - Milan announce Beckham will join them on loan on January 7, 2009.
2009: January 11 - Makes shock first start for Milan in 2-2 Serie A draw at Roma.
March 9 - AC Milan announce that under a unique "timeshare" agreement, Beckham will stay with them in Italy until the end of the season, return to the Galaxy from July to October and then rejoin the Serie A club for the rest of the 2009-10 campaign.
March 28 - Comes on as a half-time substitute against Slovakia at Wembley to win his 109th cap and break Bobby Moore's record for an outfield player.
July 20, 27 - Twice confronts fans who gave him a hostile reception in his first home games after returning to the Galaxy.
November 2 - Milan officially confirm Beckham will return in January.
2010: March 14 - Tears his Achilles tendon in AC Milan's 1-0 win over Chievo - an injury that rules him out of the World Cup.
June - Part of England's backroom staff for World Cup campaign which ends in second-round defeat to Germany.
August 11 - England career appears to be at an end when Capello tells ITV: "Probably he is a little bit old."
2011: November 20 - Wins the MLS Cup as the Galaxy beat Houston Dynamo 1-0 in the final.
December 31 - Five-year deal at the Galaxy expires.
2012: January 19 - Re-signs with the Galaxy on a two-year deal.