The former England international has been in the United States since 2016, when he signed for the Galaxy following a two-year stint at Roma.
Cole has made 55 appearances during his time at the American club, and head coach Sigi Schmid will have the 37-year-old at his disposal for another season.
"We are very excited that Ashley will be returning," said Schmid. "He's been a tremendous leader for our club and he's shown he can be successful in this league and we're confident that will continue in the season ahead."
Cole's previous deal expired at the end of the 2017 campaign.