The 38-year-old striker's departure from the Galaxy had been widely expected following the club's elimination from the Major League Soccer playoffs last month.
Ibrahimovic, who joined the Galaxy in the opening months of the 2018 campaign, announced the end of his Californian sojourn in a characteristically enigmatic post on Twitter.
"I came, I saw, I conquered. Thank you @lagalaxy for making me feel alive again," Ibrahimovic wrote. "To the Galaxy fans - you wanted Zlatan, I gave you Zlatan. You are welcome. The story continues...Now go back to watch baseball".
The Galaxy said in a brief statement the club had parted company with Ibrahimovic by mutual agreement.
"We would like to thank Zlatan for his contributions to the LA Galaxy and Major League Soccer," said LA Galaxy President Chris Klein.