The 26-year-old will join up with his new side - including former Tottenham Hotspur team-mate and current Galaxy captain Robbie Keane - in August.
"Giovani is a special player," said Galaxy head coach and general manager Bruce Arena. "He has experience and success competing at the highest level and we believe he will only continue to develop.
"We are happy to add him to our roster and have confidence he can be an integral part of our success going forward."
