Rogers, who came out in February on the same day he retired from the game, will be on the Galaxy's roster for Sunday's home match against the Seattle Sounders if his international transfer certificate arrives in time.
"I was afraid to put myself back in a situation where I felt like I was kind of an outcast I guess, or just different from people," Rogers told a news conference at the Galaxy's Home Depot Center.
"But after this whole process I've realised that everyone is a bit different, everyone has their issues."
The announcement by the Galaxy comes less than a month after National Basketball Association veteran Jason Collins became the first active athlete from the four major US men's professional sports leagues to come out publicly as gay.
Collins, however, is a free agent and has not played since his announcement after the 2012-13 NBA regular season.
Rogers said the watershed announcement by Collins, who received widespread support, including a phone call from President Barack Obama, did not influence his decision to end his brief retirement.
"Not for me," said Rogers, who was part of the US team at the Beijing Olympics and narrowly missed out on a place in the World Cup squad in 2010.
"For me it was a decision that I had to make on my own."
Rogers, a 26-year-old winger who had spells in England with Leeds United and Stevenage after first making his name in MLS with the Columbus Crew, had been training with the Galaxy for the past three weeks.
He most recently played for the United States in 2011 but struggled following a move to English second tier club Leeds in January 2012, being loaned out to third tier Stevenage before being released by Leeds earlier this year.
The Galaxy signed Rogers to a multi-year contract after acquiring the right of first refusal for him from the Chicago Fire in exchange for midfielder Mike Magee.
Rogers enjoyed a breakout season in 2008 when he scored six goals, earning all-star honors and helping the Crew win their first MLS Cup championship.
"We've been searching for the last year or two for a player that has the skills to be a flank player, play wide, add a little speed to our club," said Galaxy coach Bruce Arena.
"He offers qualities that we've been looking for so we're hopeful that in time Robbie is going to demonstrate the kind of qualities he has previously in this league."
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