Ireland international record goalscorer Keane, 36, said in a statement he was targeting one final challenge in club football before hanging up his boots for good.
Keane is one of the most successful foreign players to ply his trade in the US top flight, helping the Galaxy win three MLS Cup titles while scoring more than 100 goals in all competitions after signing for the club in 2011.
"I can confirm that after five fantastic years I will be leaving the LA Galaxy," said Keane.
"It has been a privilege to have played my part in the history of such a great club and I leave with memories that will stay with me forever."
Keane, who remains Ireland's record goalscorer with 68 from 146 appearances, said his fitness persuaded him he could still find a role elsewhere.
"I still feel as fit and sharp as ever and I am looking forward to my next adventure," he said.
"Having now retired from international football I am ready to focus everything I have on one last major challenge in club football and will be taking time out to consider my options before announcing my next move."
Galaxy coach Bruce Arena said Keane would go down in history as the "most successful international signing in this league's history."
"It is hard to put into words what Robbie Keane has meant to the LA Galaxy," Arena said.
"From day one, Keane has given everything to this team both on and off the field and has led our club to some of its greatest accomplishments."
Keane's announcement comes after former England and Liverpool captain Gerrard confirmed his departure from the club on Tuesday.