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The former England midfielder, 34, will play for the Major League Soccer club after his contract at Anfield expires.
"We were aggressive in our pursuit of Steven and look forward to his contributions on and off the field," Galaxy president Chris Klein said.
"I'm very excited to begin the next chapter of my career in the United States," Gerrard added.
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"The Galaxy are the most successful club in MLS history and I'm looking forward to competing for more championships in the years to come.
"One of the reasons I chose them was because of the success they've had recently. I want to add some medals and trophies to my collection."
Gerrard, who has won 10 trophies at Liverpool, including the Champions League in 2005, becomes the second England captain to join LA Galaxy, after David Beckham played for them between 2007 and 2012.
"We're very pleased to acquire a player of Steven's calibre, experience and character," said head coach and general manager Bruce Arena.
"He is one of the most decorated players in the world and will join our team with a wealth of success playing at the highest level of the sport.
"Steven will be an excellent example to our young players and we're excited to add him and his leadership to an already-talented roster."

The 32-year-old has joined the Conference Premier leaders from Northampton on loan until the end of the season.
"He'll come into the squad if his clearance [comes] through" said player-manager Andy Morrell.
Artell has not played since October because of an Achilles injury.
Despite his lack of games and with centre-half Martin Riley out with a hamstring injury, Morrell has not ruled out Artell starting should he eligible in time.
"He hasn't played a game for a while but he's a good pro. He knows what to do, where to be on the pitch," Morrell added.
Another midweek loan signing, striker Dele Adebola is available to make his debut after being granted international clearance.
Wrexham will be without midfielder Jay Harris who has been handed a four-match suspension following his red card at Barrow.
"We're going to miss Jay Harris for four games. It was a bit of a foolish thing to do with the state of the game," Morrell said.
We'll pick a team that we think will go and beat Alfreton - another tough game
"It happens, you've got to deal with it [and] it's a chance for someone else to stake a claim.
"Kev [Kevin Thornton] did great [and] scored a goal [against Barrow] so more than likely he will be involved as will Glen [Little].
"We'll pick a team that we think will go and beat Alfreton - another tough game."
Liverpool captain Steven Gerrard will join Los Angeles Galaxy in July, the American side have confirmed.
[NEXT_CONCEPT]
Wrexham are hopeful on loan defender David Artell will receive international clearance in time for Saturday's home game against Alfreton Town.