The Galaxy have sent the 23-year old defender, who spent last season at the StubHub Center, to the Fire and in return have acquired a conditional draft pick in the 2016 draft.
Cochrane, who made 12 MLS appearances in 2013, joined the Galaxy via the 2013 SuperDraft where he was taken with pick number 38.
Cochrane started nine times in league play last term and additionally started twice in the CONCACAF Champions League and appeared one time in the Lamar Hunt US Open Cup.
The Pennsylvania-born Cochrane will compete primarily with Segaro Gonzales for the starting left-back position at Toyota Park.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball