The Galaxy announced they were bringing him in by securing first refusal on his signature from the Chicago Fire in an exchange that sees Mike Magee move to Toyota Park.
Rogers' new club said he could be involved against Seattle Sounders tomorrow.
The 26-year-old said on the Galaxy's website: "I'd like to thank everyone at Major League Soccer, the LA Galaxy and the Chicago Fire for allowing me to return to playing the game that I love. I look forward to getting back out onto the field and continuing my soccer career as a member of the Galaxy."
Tonight he posted a picture of himself in Galaxy kit on Twitter, adding the message:
"An exciting future lies ahead, not only for me but for our society."
He become the world's most high-profile openly gay footballer, and Galaxy head coach Bruce Arena said: "We are pleased to be able to add a player of Robbie's qualities to our roster and feel that he will help improve our team now and in the future."
Rogers, capped 18 times by the United States and a 2008 Olympian, wrote on his blog in February that he had been afraid of revealing his sexuality, saying he wanted to live a new life outside of the game.
He wrote at the time: "Secrets can cause so much internal damage. People love to preach about honesty, how honesty is so plain and simple. Try explaining to your loved ones after 25 years you are gay.
"Try convincing yourself that your creator has the most wonderful purpose for you even though you were taught differently.
"Now is my time to step away. It's time to discover myself away from football."
He has previously played for Heerenveen, Columbus Crew, Leeds and, on a loan basis, Stevenage.
He was a Leeds player when he announced he was leaving the game behind.