Mahony introduced Gomez, 58, in a news conference on Tuesday at the Cathedral.
"His leadership in proclaiming the dignity and rights of our immigrant peoples has helped motivate many people to advocate for our immigrants," Mahony said.
Pope Benedict named him coadjutor for Los Angeles, which means he'll automatically become head when Mahony retires next year, and for now, he will assist the cardinal in the governance of the diocese. The church requires Mahony to retire when he turns 75 years old, which will happen next February.
Gomez was born in Monterrey, Mexico, and was ordained a priest of Opus Dei. He is one of only 22 bishops around the world belonging to the conservative order.
Gomez was somewhat emotional as he spoke of his love for Mexico and his excitement about coming to Los Angeles.
"I know that God will give me the grace to serve this local church well as Cardinal Mahony has done for so many fruitful years," he said.
"The warmth of the people here gives life to the worst we so often hear. We are not really strangers here, but only friends who have not met."
Mahony has headed the diocese for nearly 25 years, but in recent years, he dealt with a major clergy sex abuse scandal that was settled with the Church agreeing to pay a record $600 million to more than 500 alleged victims.
A massive reception for the archbishop will be held on May 26.