Cudicini, the 39-year-old former Chelsea player, has spent nearly four years at Spurs but has appeared in just one game so far this English season, in the League Cup.
"We are delighted to be able to add Carlo Cudicini to our roster," Galaxy head coach and general manager Bruce Arena told his club's website.
"Carlo is an experienced and accomplished goalkeeper who we believe will be a great addition to our team and our defensive unit."
Cudicini, who began his career at AC Milan in 1992, joined Chelsea in 1999, initially on loan, and was part of their Premier League-winning squads of 2005 and 2006.
After signing for Spurs he suffered a motorcycle accident in 2009, fracturing his wrists and injuring his pelvis. Although he recovered fitness, the club's acquisition of Frenchman Hugo Lloris this year pushed Cudicini down to third-choice at White Hart Lane behind Lloris and the American Brad Friedel.