Cudicini moved to White Hart Lane in January 2009 on a free transfer after spending nine years with London rivals Chelsea.
But the 39-year-old was restricted to just 20 appearances for Spurs because of injury - including a motorcycle crash with resulted in two fractured wrists and some pelvis damage.
The Italian stopper has fallen further down the pecking order at Tottenham and has an opportunity for some regular game time in the States.
"We have reached agreement with LA Galaxy," read a Tottenham statement.
"Carlo joined us from Chelsea in January 2009 and went on to make a total of 37 appearances. We wish Carlo all the best for the future."
Cudicini will link up with former Tottenham striker Robbie Keane at the Galaxy.
The Galaxy says the 39-year-old's move has been secured "pending the receipt of his International Transfer Certificate and work visa as well as Cudicini passing his medical.