Cruz, who has been hospitalised several times since undergoing surgery for a brain tumor in November, died at about 2100 GMT on Wednesday.
Radio and television stations said her body would be brought to Miami, where she is hailed as a national hero by the 700,000-strong Cuban exile community.
"They're bringing her here for a farewell from the Cuban community," said Joe Garcia, director of the Cuban-American National Foundation in Miami. He called Cruz "the greatest star in Cuba's history."
A vibrant and tireless performer, who would fire up her audience with her trademark shout of "Azucar," or "sugar," Cruz said only a few months ago she had no intention of giving up singing.
Top latin actor Edward James Olmos has dedicated Los Angeles's Latino film festival to the memory of the salsa queen to mark her death.
"We are celebrating the life of a great lady," Olmos told the audience gathered for the opening of the LA Latino International Film Festival.
Known for her gaudy costumes and electrifying performances, Cruz played a major role in promoting Cuban music internationally, and in February this year she received her fifth Grammy for the best salsa recording of the year.
She sang of love and life, of memories of Cuba, and of hopes democracy eventually would prevail in her communist-run homeland.
The diva of Latin song studied at the Conservatory of Music in her hometown of Havana, sang on Cuban radio programmes and became the lead singer of the legendary Sonora Matancera.
Segundo and Cruz: Latin legends
Castro never forgave her
She and the band left Cuba in 1960 and eventually settled in the United States. "Fidel Castro never forgave me," said Cruz of the Cuban president. She was never allowed to return.
In 1966 Cruz joined the Tito Puente band, and later recorded numerous solo albums. She has recorded some 70 albums, many of them gold or platinum and has received numerous awards.
In 1994, then-president Bill Clinton awarded her the National Medal of Arts, the highest US official honour, at a White House ceremony.
Her name adorns street signs, notably in Miami's Calle Ocho, emblematic of the Cuban-American community, which is also known as Celia Cruz Way.
Artists from around Latin America offered tributes to Cruz at the news of her death.
Artists of her calibre "come to the world only once every 200 years," said the Dominican composer Rafael Solano.
Her death comes three days after another prominent Cuban musician, Compay Segundo, died at the age of 95, and five days after jazz legend Benny Carter passed away after a brief illness.