The daughter of a train driver, Gheorghiu was born as Angela Burlacu in Adjud. Along with her sister Elena, she sang opera music from a very early age. At age 13, Gheorghiu went to study singing at the Bucharest Music Academy, primarily under Mia Barbu. Her graduation in 1989 coincided with the overthrow of Nicolae Ceaucescu, enabling her to seek out an international career immediately. She made her professional debut in 1992 at Covent Garden as Zerlina in Don Giovanni, followed in 1993 by debuts at the Vienna State Opera as Adina in L'Elisir D'Amore and the Metropolitan Opera as Mimi in La Bohème. Her performances of Violetta in Verdi's La Traviata at Covent Garden in 1994 catapulted her to international stardom.
Divorced from her first husband, from whom she retained her surname, Gheorghiu is now married to tenor Roberto Alagna. The couple have sung together often onstage and have made many recordings together both of duets and arias and complete operas. The two singers also starred in a film version of Puccini's Tosca directed by French film director Benoit Jacquot.