The Republic or Ireland international has signed a two-year deal with the Galaxy, reportedly worth £3m per year, and has become one of the club's designated players.
"I'm delighted, honoured and very excited to be joining the LA Galaxy," Keane told the club's official website.
"I have always wanted and play in the MLS so it's the perfect combination for me and a dream come true.
"Also when David Beckham came and trained at Spurs 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."
The Major League Soccer club will pay Spurs a fee of £2.2m for the 31-year-old.