Financial details of the move were not disclosed but British media reported that the 31-year-old striker would join on a two-year contract for 3.5 million pounds.
"I am delighted, honoured and very excited to be joining the LA Galaxy," Keane told the club website. "I have always wanted to come and play in MLS so it's the perfect combination for me and a dream come true.
"Also when David Beckham came and trained at Spurs recently he couldn't speak highly enough about the Galaxy, their fans and the league in general, so I can't wait to get over and get started," he added.
The Irishman has been a prolific scorer for several clubs after starting out at 17 with Wolverhampton Wanderers before joining Coventry City, who he joined for a then British record fee for a teenager, Inter Milan and Leeds United.
"Robbie Keane will be a great addition to our club. I have followed his career and have always respected his ability as a competitor and a goalscorer," Galaxy coach Bruce Arena said.
"I believe that he brings qualities in and around the penalty area that we have been lacking."
Keane leaves Spurs after his second spell at the London club Having scored 123 in 306 games in all competitions according to the club website.
His first six-year period, which included winning the League Cup, ended with a $30 million move to Liverpool in July 2008 only for the striker to return seven months later.
During the second spell Keane, who played for Ireland at the 2002 World Cup, struggled to hold down a starting spot and went out on loan to Celtic and West Ham United.
The deal is subject to Keane receiving a visa and Galaxy must make an adjustment to their squad to incorporate the striker as a designated player.
The rule, also known as the Beckham Rule, allows teams to sign two players outside the MLS salary cap and three paying an extra so-called "luxury tax."
