The Major League Soccer club said in a statement it had declined to exercise an option to re-sign Cole for the 2019 season.
Cole, 37, signed for the Galaxy in 2016 following a glittering club and international career that included stints with Arsenal, Chelsea and Roma.
The Galaxy meanwhile confirmed that 16 members of its 2018 roster were due to return next season, including Swedish striker Zlatan Ibrahimovic.
Ibrahimovic’s future with the club has come under scrutiny in recent weeks with reports in Italy linking him to a possible return to Serie A with AC Milan.
Ibrahimovic, who scored 22 goals in 27 games for the Galaxy this season, said earlier this month that he is optimistic of returning to Los Angeles in 2019, but wants the club to challenge for silverware.
“For me to return, I want to be able to challenge for the trophy,” Ibrahimovic said. “I’m not here for a vacation. I’m here for the challenge. I want to feel I have a chance to be the best in MLS – my team, not me, because I am the best.”