The fee for the 31-year-old Keane was not disclosed, but it is believed to be in the region of $5.7 million, with Keane signing a two-year contract.
Los Angeles already has three Designated Players on its roster, which is the maximum amount allowed, so the club will have to make a change prior to adding Keane to its roster.
The move is expected to be a trade of striker Juan Pablo Angel, which would free up a spot for Keane.
"I am delighted, honored and very excited to be joining the L.A. Galaxy," Keane said. "I have always wanted to come and play in MLS so it's the perfect combination for me and a dream come true. My family and I have already been made to feel very welcome in telephone calls from Tim Leiweke and Bruce Arena. 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."
Keane is Ireland's all-time leading scorer, having tallied 51 goals in 108 appearances for his country, while also enjoying a good spell at Tottenham from 2002-08 that saw him net 107 goals in 254 matches for Spurs.
"Robbie Keane will be a great addition to our club," said Galaxy general manager and head coach Bruce Arena. "I have followed his career and have always respected his ability as a competitor and a goalscorer. I believe that he brings qualities in and around the penalty area that we have been lacking. Hopefully, he will be another piece of the puzzle in our quest for the Supporters' Shield and an MLS Cup championship as well as to advance to the next round of the CONCACAF Champions League."