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.
"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."
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."
