State television announced Niyazov died of heart failure. He was 66.
According to the country's constitution the acting head of state is speaker of the Halk Maslahaty (People's Council) Ovesgeldy Ataev.
Constitutionally, Ataev can remain as acting head of state no longer than three months and must organize a presidential election during that time.
Also according to the constitution, Ataev cannot run for the presidency.
State television did not mention Ataev during its broadcast.
State television announced a period of mourning and the date for Niyazov's funeral.
"It has been decided that our great leader will be buried on Sunday, December 24," a reporter said. "Seven days of mourning have been announced including the seventh day after the death of our great leader."
State television reported that Health Minister Gurbanguly Berdymukhammedov is in charge of the commission preparing a state funeral for Niyazov.
Known as Turkmenbashi (Leader of the Turkmen), Niyazov had ruled Turkmenistan since 1985, when it was a Soviet republic, and oversaw its transition to independence. He ruled Turkmenistan with an iron fist, creating an elaborate personality cult around himself. In 1999, the country's legislature declared him president for life.
Niyazov had major heart surgery in 1997, and last month he acknowledged publicly for the first time that he had heart disease.