Cole left Serie A team AS Roma this month after his contract was cancelled by "mutual consent". The 35-year-old had made just 11 league appearances for the Italian club after signing for them in July 2014.
Cole will link up in Los Angeles with his former England team-mate Steven Gerrard and 32-year-old Belgian defender Jelle Van Damme, who signed for the club on Tuesday.
"Ashley is one of the world’s most successful defenders and has played at the highest level of competition throughout his career," said Galaxy head coach Bruce Arena.
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"He can provide our defence with valuable experience. We look forward to his contribution to our club this season."
Cole made 107 appearances for England and was part of Chelsea's Champions League winning team in 2012.
Despite Cole's lack of action over the past year, Arena believes he is in shape and motivated.
"He’s very fit and has a burning desire to get back on the field and prove to people that he can still play. I have a hard time believing that he won’t be one of the better left backs in our league," he told the team's website.
Cole raised eyebrows in the United States when, after signing for Roma in 2014, he said he had turned down offers from MLS because he was "not ready to relax on a beach yet".
"Whether you think it’s a risk or a gamble, these are the risks and gambles that you take," Arena said.
"There is a real upside of having Ashley Cole with the LA Galaxy."
(Reporting by Simon Evans, editing by Alan Baldwin)
