The 37-year old former Galaxy player, who retired in 2010, has served as the senior director of the Galaxy Academy before being promoted to vice-president in February 2012 but has now taken the reins at The Home Depot Center.
"We have always been impressed with Chris' commitment and desire to excel on the business side of sports, and we have great confidence and faith that he will take the LA Galaxy to new levels," said AEG President and CEO Tim Leiweke.
"We admire his passion and loyalty to the brand and his desire for the Galaxy to be the greatest soccer club in the history of this sport in this country. What makes Chris even more valuable to the Galaxy is his ability to understand our academy system, our development system and the partnership he has with Bruce will allow the Galaxy to continue to compete for championships year after year."
Klein added: "I am thrilled with this opportunity and excited to continue working with the great group of individuals we have on our staff.
"The Galaxy's best days are ahead of us and I am thankful that Tim and his team at AEG have the confidence in me to help lead us into the future."