Arena joined the club in 2008 and has led them to two MLS championships.
"Bruce is one of the finest coaches in the history of soccer in the United States," Galaxy president Dan Beckerman said in a statement.
"His commitment to the LA Galaxy, the club's winning tradition and continued excellence on and off the field is unrivalled. We look forward to the team's continued success under Bruce's management."
Arena also managed the United States national team from 1998 to 2006.