Cordileone is currently bishop of Oakland, Catholic San Francisco reported. He will replace Archbishop George Niederauer, who has led the archdiocese since 2006.
The pope accepted the 76-year-old Niederauer's resignation. Niederauer said Cordileone will be installed on Oct. 4, feast day of San Francisco's patron saint, St. Francis of Assissi.
Since last year Cordileone has headed a subcommittee of the U.S. Conference of Catholic Bishops charged with defending traditional marriage. He was also one of the authors of Proposition 8, the referendum that overturned a court decision legalizing same-sex marriage in California, the Italian news agency ANSA reported.
A native of San Diego, Cordileone was ordained there in 1982. He has split his time between California and Rome, where he studied and from 1995 to 2002 served as an official of the Signatura, the church's highest judicial body.
Cordileone was named an auxiliary bishop in San Diego in 2002 and bishop of Oakland in 2009.
Astronomers offer more expansive view of universe
Duggar sisters unveil Christian dating rules in new book