According to a report on the Slipped Disc music news site, Schiff was artistic director of the Northern Sinfonia in England from 1990 to 1996. He also worked as the chief conductor of the Copenhagen Philharmonic and the Orchester Musikkollegium Winterthur.
He was well known for his interpretation of the Schumann concerto and Bach's cello suites. He had given up playing after his stroke in 2008, but continued to teach and conduct until his health declined.
In an interview with Slipped Disc last year, fellow cellist Steven Isserlis described Schiff's “crystal intelligence and his unique sense of humour”.
He told the website: “I was complaining (as usual) about the pressures of performing the Bach suites. He looked at me, and said quietly: ‘Bach saved my life’.
“I asked him what he meant and he told me that a few years ago, he had a serious stroke, and was in danger of losing all mobility on his left side.
"As soon as he got to hospital, and realised what was happening, he started (almost instinctively, I imagine) to go through the fingerings of the Prelude to Bach’s first suite, moving his fingers ceaselessly to the imaginary music.
"He did this for about 20 hours a day, he thinks; and gradually his whole body came back to life, powered by those fingerings.
“Today, you would never guess that he could have been half-paralysed, possibly even incapable of speech – or worse. The miracle of Bach – and of Heinrich.”
Schiff was born in Gmunden, Austria in 1951. He was 65 years old.