The former England captain's five-year contract with the Major League Soccer side expired last month and he had been linked with a move to
However, the 36-year-old has now signed a new two-year deal with
And he insists he feels there is still more to achieve in America as he enters the final chapter of his career.
"It was a decision that I didn't take lightly," he said on a YouTube and Google+ webchat. "I had other offers and at 36 you don't expect to get these.
"The future of the game is in the US and where my family is happiest. I love living in the LA, I love living in America.
"For me, soccer's the number one sport around the world, apart from America. I want to get soccer to another level in the US. I've felt a change in the last two years and don't want to walk away from it - I want to continue to be a part of that growth."