Rexach was born and raised in Santurce, Puerto Rico. Her parents were Julio E. Rexach of Fajardo, and María Teresa González, of San Juan, Puerto Rico. There she attended public school and received her primary education. She then went to a private school where she finished her secondary education before attending the Central High School of Santurce. During her high school years, when she was 14 years old, she wrote several poems which were to become part of her musical compositions. She amazed her teachers when she composed "Di, Corazón" (Tell me, Heart) and "Matiz de Amor" (Calm Love). Rexach also learned how to play musical instruments, such as the guitar, the piano and the saxophone at a young age.
Rexach enrolled in the University of Puerto Rico where she was going to take a pre-legal course, however when the United States entered World War II in 1942, Rexach dropped-out of the university and joined the United States Army as a member of the WACS (Women Army Corps Service) where she served as an office clerk.
After the war, Rexach was discharged from the armed forces. She married William Riley with whom she had three children which included actress/singer Sharon Riley. The marriage eventually ended in a divorce and she returned to Puerto Rico where she went to work for a radio station as a comical script writer, first for producer Tommy Muñiz, and later for comedian Ramón Rivero "Diplo". She was the founder of the first Combo in Puerto Rico consisting entirely of women. They were named Las Damiselas, and besides Rexach included: Idalia Rosario, Marta Romero, Millita, Elena Rita Ortiz, and Ketty Cabán.
In 1951, Rexach had a newspaper column called "A Sotto Voce" where she was a music critic. She was also a co-founder of The Puerto Rican Society of Authors, Composers and Music Editors (Sociedad Puertorriqueña de Autores, Compositores y Editores de Música). She was its Secretary Director, a position which held until the day of her death.
The tones of Rexach's compositions varied from the soft and romantic to the harsh and tormented. Among the songs written by her and which were "hits" in Puerto Rico and aboard were: "Alma Adentro" (Inner Soul, actually a homage to a brother who died in an accident), "Idilio", "Olas y Arenas" (Waves and Sands), "Mi Versión" (My Version), "Nave sin Rumbo" (Wandering Ship), "Di, Corazón" and "Matiz de Amor". She even wrote a humorous novelty song, "Cuchú cuchía", which features Rafael Hernández Marín as a co-composer.
Sylvia Rexach, was an alcoholic at the time of her death October 20, 1961, in San Juan, Puerto Rico. Her death certificate states the cause as an intestinal obstruction, complicated by a duodenal atresia.
Her compositions have been recorded by many other artists, such as Marco Antonio Muñiz, Danny Rivera, Gilberto Monroig, Chucho Avellanet, Lucecita Benítez, Juan Luis Barry, Linda Ronstadt, Ednita Nazario, Lourdes Pérez and Lunna. Two television specials were made about Sylvia's life, "Sylvia, en tu Memoria" (Sylvia, in your Memory) and Ángela Meyer's "El fondo del Dolor" (In the Deepest Pain) starring Sharon Riley, Sylvia's daughter.
In 2001, Rexach was posthumously inducted into the International Latin Music Hall of Fame. There is a theater named after Rexach in San Juan and in the Luis A. Ferre Center of Fine Arts, there is a Sylvia Rexach Cafe Theater.
In May 29, 2014, The Legislative Assembly of Puerto Rico honored 12 illustrious women with plaques in the "La Plaza en Honor a la Mujer Puertorriqueña" (Plaza in Honor of Puerto Rican Women) in San Juan. According to the plaques the following 12 women, who by virtue of their merits and legacies, stand out in the history of Puerto Rico. In May 29, 2014, The Legislative Assembly of Puerto Rico honored 12 illustrious women with plaques in the "La Plaza en Honor a la Mujer Puertorriqueña" (Plaza in Honor of Puerto Rican Women) in San Juan. According to the plaques the 12 women, who by virtue of their merits and legacies, stand out in the history of Puerto Rico. Rexach was among those who were honored.