Kio held honorary titles in Russia and Georgia, and remains the only illusionist to be awarded an Oscar (Belgium) for best artist. He also was a member of the International Brotherhood of Magicians.
"The artist died after a short illness at the age of 62," the company said.
He was one of the most prominent artists in the former Soviet Union and Russia.
Born March 13, 1944, Kio was brought up in a family of circus performers. His parents worked together as magicians all their lives.
Kio attended a Moscow school until the age of 15, then traveled around and studied at various schools throughout the country, finally graduating in Georgia. He was also a passionate football player.
Kio began performing at the age of 15 and enjoyed immediate fame. He was so popular that he was obliged to put on 500-600 shows a year all over the Soviet Union for 30 years.
He was often invited to work on television, and had his own New Year program in the 1980s that brought together pop music, theater and film stars.
In 1989, Kio left the state circus company and opened his own firm organizing tours for his and other artistic teams.
In 1994, Kio staged a gala show, Magician of the 20th Century, devoted to his father's 100th birthday.
He was the first to form a professional ballet troupe of 18 people in a circus.
Kio was married three times, the last time for 20 years.
His first brief marriage to the only daughter of Soviet leader Leonid Brezhnev, Galina, lasted only nine days. In his second, 11-year marriage, Kio had a daughter who later performed in his show as a ballet dancer.