The appointment was described as the Pope's revenge on Hollywood for filming The Da Vinci Code.
Benedict XVI's choice comes after Colombia Pictures depicted Opus Dei as a secret society of murderous monks who, according to author Dan Brown, were trying to cover up the truth of Jesus's secret affair with Mary Magdelene.
The appointment will give Opus Dei enormous influence in the American Church and Vatican, and is the most senior appointment for a member of the group.
It will also lead to Mexican-born Gomez, formerly the Archbishop of San Antonio, Texas, becoming the first Latin American US cardinal, a position that will give him influence in Rome and the right to vote at a papal conclave.
The choice is likely to dismay the Catholics of Hollywood, which falls within the archdiocese. The reigning archbishop, Cardinal Roger Mahony, avoided confrontation, but Archbishop Gomez is less likely to duck controversy.
Opus Dei, which he joined in 1978, is seen as one of the most devout of all the Catholic groups. Some of its priests practise self-flagellation while praying to the Virgin Mary and also wear a cilice – a spiked garter – to help them to mortify the flesh and avoid sexual sins.
One of Archbishop Gomez's primary tasks will be to deal with the fallout from the abuse crisis.
None of the 2,000 priests of Opus Dei, which has the status of a "personal prelature" of the Pope, has ever been embroiled in a sexual scandal.
The Archdiocese of Los Angeles, however, is one of the worst afflicted by the clerical sexual abuse crisis that has convulsed the US Church since 2002.
Three years ago Cardinal Roger Mahony, the reigning archbishop, agreed to a record-setting £430 million settlement with more than 500 alleged victims of clergy abuse.
A federal grand jury is also investigating how the Archdiocese of Los Angeles handled claims of abuse.
Archbishop Gomez, 58, will work alongside Cardinal Mahony and take over when he retires next year. One of his first tasks will be to reform the priesthood.
"I welcome Archbishop Gomez to the Archdiocese of Los Angeles with enthusiasm and personal excitement," Cardinal Mahony said.
In a statement posted on the Los Angeles archdiocese website, Archbishop Gomez said: "When I was collecting my thoughts for today, I wrote down that the Archdiocese of Los Angeles is one of the great Catholic communities in the United States. But it’s really much more than that. It’s one of the great Catholic communities in the world. Los Angeles, like no other city in the world, has the global face of the Catholic Church.
"That fact invites us to do two things: first, to thank God for our diversity and the energy it creates; and second, to commit ourselves more deeply to the things that unite us – a zeal for Jesus Christ; confidence in the Gospel; reverence for the Eucharist; service to the poor; defence of the unborn child, the immigrant and the disabled; and a love for the Church as our mother and teacher.
"These are the things that have purified and renewed the Church in every generation. And being with all of you now as part of Cardinal Mahony’s ministry is the greatest gift I've received in my life next to the priesthood itself."
Archbishop Gomez is one of 22 bishops worldwide who belong to Opus Dei, a movement founded in 1928 by St Jose Maria Escriva, a Spanish priest, to help Catholics to find salvation through their ordinary working lives.
Its penitential practices, courting of the professional classes, and its loyalty to the Pope has incurred the distrust of many within the Church and outside it.
Dan Brown's best-selling novel was adapted for the big screen in 2006 by Oscar-winning director Ron Howard and starred Tom Hanks, Audrey Tautou and Sir Ian McKellen.
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