The exact cause of his death was not reported, but the British broadcaster said Tavener had been in poor health for years after suffering a stroke in 1979 and a heart attack in 2007. He also was diagnosed with Marfan Syndrome in 1990.
Throughout all his health crises, however, the London native continued to work until shortly before he died, the BBC said.
The two-time Mercury Prize nominee first achieved fame for his avant-garde oratorio "The Whale," which was released by The Beatles on their Apple record label in 1968.
His "The Protecting Veil" topped the classical music charts for several months in 1992 and his "Song For Athene" was played at the 1997 funeral of Princess Diana.
"I have always loved hymns, since I was a 6-year-old, playing them on my grandfather's pipe organ," Tavener wrote in an undated essay on his website. "I had a very inspiring music master at Highgate who played hymns wonderfully slowly and interpreted them like huge tone poems. Today, people play hymns far too clinically. The best ones are noble and majestic, with inspired tunes and text, like 'When I Survey the Wondrous Cross,' 'Eternal Father Strong to Save,' 'Love Divine and Lead Kindly Light.'"
"He could bring an audience to a deep silence which is a very rare gift," composer John Rutter told the BBC. "He believed that music was for everybody and was a prayer."