In 1950, Cruz made her first major breakthrough, after the lead singer of the Sonora Matancera, a renowned Cuban orchestra, left the group and Cruz was called to fill in. Cruz was hired permanently by the orchestra, but 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 15 years she was a member, the band traveled all over Latin America, becoming known as "Café Con Leche" (coffee with milk). Cruz became known for her trademark shout "¡Azúcar!" ("Sugar!" in Spanish). The catch phrase started as the punch line for a joke Cruz used to tell frequently at her concerts. Once, she ordered cafe cubano (Cuban coffee) in a restaurant in Miami. The waiter asked her if she'd like sugar, and she replied that, since he was Cuban, he should know that you can't drink Cuban coffee without it! After having told the joke so many times, Cruz eventually dropped the joke and greeted her audience at the start of her appearances with the punch line alone. In her later years, she would use the punch line a few times, to later say: "No les digo más 'Azúcar', pa' que no les dé diabetes!" which means "I won't say 'Sugar' anymore so that you won't get diabetes".
With Fidel Castro assuming control of Cuba in 1959, Cruz and her husband, Pedro Knight, refused to return to their homeland and became citizens of the United States. 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, Puente and Cruz later joined the Vaya Records label. There, she joined accomplished pianist Larry Harlow and was soon headlining a concert at New York's Carnegie Hall.
Cruz's 1974 album with Johnny Pacheco, Celia y Johnny, was very successful, 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, Cruz had the opportunity of visiting England, France, Zaire (Today's DR Congo), and to return to tour Latin America; her performance in Zaire is included in the film Soul Power. In the late 1970s, she participated in an Eastern Air Lines commercial in Puerto Rico, singing the catchy phrase ¡Esto sí es volar! (This really is flying!).
Celia Cruz used to sing the identifying spot for WQBA radio station in Miami, formerly known as "La Cubanísima": "I am the voice of Cuba, from this land, far away,..., I am liberty, I am WQBA, the most Cuban! (Yo soy de Cuba, la voz, desde esta tierra lejana, ..., soy libertad, soy WQBA, Cubanísima!) During the 1980s, Cruz made many tours in Latin America and Europe, doing multiple concerts 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 feature film Salsa, alongside Robby Draco Rosa.
In 1990, Cruz won a Grammy Award for Best Tropical Latin Performance - Ray Barretto & Celia Cruz - Ritmo en el Corazon. She later recorded an anniversary album with la Sonora Matancera. In 1992, she starred with Armand Assante and Antonio Banderas in the film The Mambo Kings. In 1994, President Bill Clinton awarded Cruz the National Medal of Arts. In 2001, she recorded a new album, on which Johnny Pacheco was one of the producers. On July 16, 2002, Cruz performed to a full house at the free outdoor performing arts festival Central Park SummerStage in New York City. During the performance she sang, "Bemba Colora." A live recording of this song was subsequently made available in 2005 on a commemorative CD honoring the festival's then 20 year history entitled, "Central Park SummerStage: Live from the Heart of the City". Cruz appeared on the 2006 Dionne Warwick album My Friends & Me.
On July 16, 2003, Cruz died of brain cancer at her home in Fort Lee, New Jersey, at the age of 77. She was survived by her husband, Pedro Knight (died February 3, 2007). She had no children. After her death, her body was taken to lie in state in Miami's Freedom Tower, where more than 200,000 fans paid their final respects. Her body was returned to New Jersey where tens of thousands of fans paid tribute to her at the funeral home. A service was held for her in St. Patrick's Cathedral. She was interred in a private mausoleum at Woodlawn Cemetery in the Bronx. An epilogue in her autobiography notes that, in accordance with her wishes, Cuban soil which she had saved from a visit to Guantánamo Bay was used in her entombment.