Keane had been in discussions with the MLS club over a move after it became clear that he was surplus to requirements at White Hart Lane.
The Republic of Ireland captain admitted earlier this week that he thought his time at Tottenham was coming to an end, and the move to join David Beckham's team 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".
The Galaxy currently have David Beckham, Landon Donovan and Juan Pablo Angel registered as theirs, but former Aston Villa striker Angel is thought to be negotiating a release from the club.
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 fans' favourite.
He then moved to Liverpool for ?20million but returned to north London within six months after failing to impress at Anfield.
Keane played regularly under Harry Redknapp during his first season back but the arrival of Rafael Van der Vaart last summer reduced his first-team opportunities and he was shipped out on loan to West Ham, where he failed to impress.
Source: Team Talk
Source: Team Talk