Prime Minister Elio Di Rupo made the announcement Sunday, and the country's media said Mortier died the day before at his home in Brussels after a protracted battle with pancreatic cancer.
Di Rupo called Mortier a "visionary and generous personality," praise echoed by French President Francois Hollande, who said, "He never stopped fighting, until the end of his strength, for culture in Europe."
Teatro Real, where Mortier was serving as artistic adviser, said in a statement: "He contributed to promoting Spain's operatic and cultural landscape and placing the Teatro Real among the world's leading international opera houses."
A baker's son from a humble background, Mortier was enchanted with opera from a young age and tried to revolutionize it at revered institutions, from the National Opera of Belgium to the Salzburg Festival.
The artist became the director of Belgium's National Operation, known as La Monnaie, in 1981, steering it away from "bourgeois" entertainment and to international recognition and acclaim.
He did so without relying on "star" singers, some of whom he considered little more than hired voices, and instead looked for the best stage directors who would immerse themselves in his vision.
At a time when much of opera was still ensconced in the regalia of "old" art, Mortier relied on people such as director Peter Sellars and composer Philip Glass to push the artistic envelope, sometimes to a breaking point.
Mortier oversaw a sumptuous renovation of the Brussels opera house and projects such as the world premiere of "The Death of Klinghoffer" on the 1985 killing of a handicapped American Jew by Palestinian terrorists aboard the cruise ship Achille Lauro.
Then he explored new frontiers.
He succeeded Herbert von Karajan at the Salzburg Festival in 1992, and initially created a storm with daring productions before he left a decade later as a grand figure in the world of opera.
It was on to Paris, and the plan was to crown his career at the New York City Opera. When that backfired over financial issues, he went on to work at the Teatro Real in Madrid, where he was appointed artistic director in 2009.
In January 2010 his title was changed to artistic adviser in a dispute with Spain's government over his successor.
Still, Mortier remained a driving force at Teatro Real and he was behind Charles Wuorinen's opera "Brokeback Mountain," adapted from the short story by Annie Proulx, who also wrote the libretto. The opera premiered in Madrid in late January.
Teatro Real said Mortier worked to the end and when unable to attend a news conference in late February, he still managed to send a text so it could be read out.
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Harold Heckle contributed from Madrid.