Keane had been in discussions with the MLS club over a move after it became clear he was surplus to requirements at White Hart Lane. The Republic of Ireland captain admitted earlier this week he thought his time at Tottenham was coming to an end, and the move to join Beckham's team in a £3.5million transfer was finally completed on Monday evening.
"Tottenham can announce that it has reached agreement with Major League Soccer side LA Galaxy for the permanent transfer of Robbie Keane," a statement on the Spurs website read.
Negotiations between the two parties had been held up by MLS rules, which state that any franchise must have only three high-earning squad members, known as "designated players".
Keane will join Beckham, Juan Pablo Angel and Landon Donovan, all three of whom have played in the Premier League, at the Galaxy - although Angel is believed to be negotiating a release.
He revealed a chat with new team-mate Beckham was key to persuading him to move to the United States.
"I am delighted, honoured and very excited to be joining the LA Galaxy," Keane told The Galaxy's website. "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 (Galaxy owner) Tim Leiweke and (manager) Bruce Arena.
"Also when David Beckham came and trained at Spurs (in January) 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's departure brings to an end his second spell at White Hart Lane. The 31-year-old made 254 appearances for Spurs during his first stint between 2002 and 2008, during which time he scored 107 goals and quickly became a fan favourite.
Source: PA
Source: PA