Parra, the son of a schoolteacher, was born in 1914 in San Fabián de Alico, near Chillán, in Chile. He came from the artistically prolific Parra family of performers, musicians, artists, and writers. His sister, Violeta Parra, was a folk singer, as was his brother Roberto Parra Sandoval.

In 1933, he entered the Instituto Pedagógico of the University of Chile, where he qualified as a teacher of mathematics and physics in 1938, one year after the publication of his first book, Cancionero sin Nombre. After teaching in Chilean secondary schools, in 1943 he enrolled in Brown University in the United States to study physics. In 1948, he attended Oxford University to study cosmology. He returned to Chile as a professor at the Universidad de Chile in 1952. Parra served as a professor of theoretical physics at the University of Chile from 1952 to 1991, and was a visiting professor at Louisiana State University, New York University, and Yale University. He read his poetry in England, France, Russia, Mexico, Cuba, and the United States. He published dozens of books.

Parra was proposed on four occasions for the Nobel Prize in Literature. On 1 December 2011, Parra won the Spanish Ministry of Culture’s Cervantes Prize, the most important literary prize in the Spanish-speaking world. On 7 June 2012, he won the Pablo Neruda Ibero-American Poetry Award.

Parra died on 23 January 2018, at 7:00 am, in La Reina in Santiago de Chile, at the age of 103.