The statue, a first for an MLS player, honours the former England captain who was the first big European name to join the league, boosting its popularity and paving the way for other global stars to make the leap.
Beckham won back-to-back championships in 2011 and 2012 during his six years and 98 appearances with the Galaxy.
"Our city, our home," Beckham said outside the Galaxy's home stadium, the Dignity Health Sports Park in Carson, before their opener against the Chicago Fire.
"From day one when my family arrived in this city, we felt at home and for that we will be forever grateful.
"When I talk about LA Galaxy and when I talk about LA, I talk about it as family because it is a big family."
The statue unveiling came a day after Beckham helped open a soccer field for underprivileged youth in downtown Los Angeles.
"Taking care of the next generation of soccer stars in this country is really important and we did it in a community that really needed support and a safe environment for children," added 43-year-old Beckham, his parents and wife Victoria among the audience.
Former Galaxy team mate Robbie Keane paid tribute to Beckham as a loyal friend and family man.
"The David Beckham the public know is a global superstar and icon throughout the world," said Keane.
"But the one I know is even better."
Retired NBA star Kobe Bryant also gave a video-taped tribute to the former Manchester United and Real Madrid midfielder Beckham, the owner of expansion side Inter Miami CF, which is set to join the MLS in 2020.
"He was the first truly big name to come to the states and really draw attention to the sport," said the former Los Angeles Lakers forward.
(Reporting by Rory Carroll; Editing by Ian Ransom)
