Moiseyev had been unconscious for the past three days and died in a Moscow hospital, said Yelena Shcherbakova, director of the Moiseyev Dance Company, the ITAR-Tass news agency reported.
Moiseyev, called the king of folk dance, attracted the West to Russian culture at a time of deep political hostility and won standing ovations around the world.
He brought traditional folk dance onto the professional stage by combining ethnic moves with classic ballet. His numbers - from the Russian peasant girl dance to the Greek Sirtaki - were hailed as promoting peace and tolerance by showing that each culture is unique. He amazed Americans with his take on rock 'n' roll and square dance.
Moiseyev had been in poor health in recent years and was rarely seen in public. Looking very frail, he made an appearance at a Moscow concert to celebrate his 100th birthday last year.
President Vladimir Putin has expressed his condolences, the Kremlin said.
Moiseyev was born Jan. 21, 1906, in Kiev, the capital of Ukraine, and enrolled in a dance school at age 14. He showed outstanding talent and was transferred to the Bolshoi Theater choreography school in Moscow, where he became a Bolshoi dancer in 1924.
He soon was ousted from the Bolshoi because of his love of daring experiments, and he began to choreograph and direct independent performances.
In 1937, he founded the Moiseyev Dance Company. Its first performance was a groundbreaking exploration of the music, culture, traditions and costumes of the numerous ethnic groups of the former Soviet Union.
Moiseyev's company inspired the creation of folk dance companies in many other countries.
He also is credited with pioneering the genre of gymnastic performance - a blend of dance and acrobatic elements - which for decades has been used in parades and celebrations in Russia and throughout the world.
Although he refused to join the Communist Party, he was favored by Soviet leaders, including Joseph Stalin, and his dance company was the first to travel abroad, even before the Bolshoi Ballet.
A funeral is planned for Wednesday, Shcherbakova of the Moiseyev company said.
Moiseyev is survived by his wife.
The choice of the city of Helsinki is not incidental as the capital of Finland had hosted US-Soviet negotiations on the limitation of nuclear stockpiles in 1969