Cruz was born in the Santo Suarez neighborhood of Havana. When she was a child, she earned her first pair of shoes by singing to a couple of tourists.
As a teenager, her aunt took her and her cousin to cabarets to sing, however her father encouraged her to keep attending school, in hopes that she would become a teacher. But a teacher told her that as a entertainer Cruz could make in one day what most teachers make in one year.
Cruz began singing on talent contests, often winning cakes and also opportunities to participate on more contests. In 1950, she made her first major breakthrough the leading singer of the famous Cuban band La Sonora Matancera returned to Puerto Rico, and Cruz was called to fill in. Hired permanently by the orchestra, she wasn't well accepted by the public at first. However, the orchestra stood by their decision, and soon Cruz became famous throughout Cuba. During the fiften years she was a member, the band travelled all over Latin America, becoming known as Cafe Con Leche ("coffee with milk"). Cruz became known for her shout "ˇAzúcar!" ("Sugar!").
In 1960, in the aftermath of the Cuban Revolution, Cruz moved to the United States. In 1961, she and her orchestra began performing at the Hollywood Palladium. The following year, she married her lead trumpeter, Pedro Knight. In 1965, Cruz and her husband left the orchestra. Her solo career advanced, while Knight's career languished, and eventually, he became her manager. She was by then a US citizen and never returned to Cuba.
In 1966, Cruz and Tito Puente began an association that would lead to eight albums for Tico Records. The albums were not as successful as expected, however, and later, Cruz joined the Vaya Records label. There, she joined accomplished pianist Larry Harlow and was soon headlining a concert at New York's Carnegie Hall.
Her 1974 album, with Johnny Pacheco, Celia y Johnny, went gold, and Cruz soon found herself in a group named the Fania All Stars, which was an ensemble of salsa musicians from every orchestra signed by the Fania label (owner of Vaya Records). With the Fania All Stars, Celia had the opportunity of visiting England, France, Zaire, and to return to tour Latin America. In the late 1970s, she participated in an Eastern Airlines commercial in Puerto Rico, singing the catchy phrase ˇˇˇEsto sí es volar!!! (This really is Flying!!!).
During the 1980s, Cruz made frequent tours in Latin America, doing multiple concert and television shows wherever she went, and singing both with younger stars and stars of her own era. She began a crossover of sorts, when she participated in the 1988 Hollywood production of Salsa, alongside Draco Cornelio Rosa.
In 1991, Cruz sang along with Cuban pop star Martika on the song "Mi Tierra", about a young Cuban-American woman longing for her homeland. The song became a crossover hit in over more then ten countries, winning Cruz a legion of younger fans. She later recorded an anniversary albums with La Sonora Matancera.
In 2001, she recorded a new album, of whom one of the was Johnny Pacheco was one of the producers of the album.
In early 2003, she had surgery to correct knee problems that she had for a few years, and she intended to continue working indefinitely. However, in July of that year, she died of a cancerous brain tumor at her home in Fort Lee, New Jersey. After her death, her body was taken on a tour of US cities with large Cuban populations so that her many fans could pay their final respects.