The Chile World Cup star signed in a deal worth around £3.3 million from Club America of Mexico.
He told the Sunday Mercury: "I am very proud to get the chance to play in such an important league, the most watched in the world, and where the best football is being played.
"Birmingham watched me a lot, for a long time, and made a very big effort to sign me. I am happy for that and I hope to repay them.
"I like to play on the left but I will do it where the coach wants me to.
"From speaking to him, he wants me to play where I like most and feel comfortable, and that is on the left."