Ortega was made cardinal in 1994 and successfully negotiated modest openings for the Church in a country that for years was officially atheist.
He oversaw the historic 1998 visit by Pope John Paul II and the 2012 trip by Benedict.
But some dissidents have criticized him for not taking a more confrontational stance toward the Communist-run government.
His style has tended toward quietly negotiating with authorities. In recent years he was key to a deal under which the last of 75 government opponents still behind bars after a 2003 crackdown were released. Most went into exile in Spain, though some remain in Cuba.
Enrique Lopez Oliva, an expert on the Church at the University of Havana, said if the church hews to past precedent, Garcia will likely be transferred from Santiago, the country's second-largest city, to the Havana diocese and elevated to cardinal whenever Ortega's resignation is accepted.
Garcia "is moderately critical of the government," Lopez Oliva said. "Although with some differences, he is going to continue the same line as Ortega and try to recover space for the survival of the institution through dialogue with the government."
Ortega was one of a number of priests who were harassed during the 1960s and for a time was sent to a labor camp.
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Andrea Rodriguez on Twitter: www.twitter.com/ARodriguezAP