Alexander Salazar was born in San Jose, Costa Rica. His family came to the United States in 1953 and settled in Los Angeles. He became a U.S. citizen at the age of 18.

Salazar studied at California State University, Los Angeles, and later at Immaculate Heart College, Los Angeles, where in 1978 he received a bachelor's in bilingual studies.

In 1977, he entered St. John's Seminary in Camarillo. He was ordained a priest in June 1984.

Bishop-designate Salazar has served in a number of pastoral and archdiocesan assignments, including being pastor of St. Teresa of Avila Parish.