Regarded as one the finest baritones of his age, he was diagnosed with brain cancer two-and-a-half years ago.
Born in Siberia, he sang in a heavy metal band before making his name in opera as the winner of BBC Cardiff Singer of the World in 1989.
He beat Bryn Terfel in that competition and went on to perform in all the world's major opera houses.
Hvorostovsky, described by Elle magazine as the "Elvis of opera", became especially renowned for his portrayal of the title character in Tchaikovsky's Eugene Onegin.
"On behalf of the Hvorostovsky family, it is with heavy hearts that we announce the passing of Dmitri Hvorostovsky - beloved operatic baritone, husband, father, son, and friend - at age 55."
He died peacefully surrounded by his family near his home in London, the statement said.
"May the warmth of his voice and his spirit always be with us," it added.
Vienna State Opera director Dominique Meyer said: "This is a very, very sad day for all of us. With Dmitri Hvorostovsky we lost an outstanding singer and a real friend."
The Russian Embassy in London has opened a book of condolence, and tributes have been paid by fans and musicians on social media.