Wilcock was born at Buenos Aires.

He studied at the Universidad de Buenos Aires from which he graduated as a Civil Engineer in 1943. That same year he started to work for a railroad company then in expansion in the western parts of Argentina. The experience would be short-lived, as Wilcock resigned a year later. His first known literary work and accomplishment came in 1940 under the title Libro de poemas y canciones ("Book of Poems and Songs") which earned the Martín Fierro, a prize given by the Argentine Society of Writers (SADE). The same work would also win the prestigious Municipal Award of Literature given by the City of Buenos Aires. Soon Wilcock would see himself surrounded by some of the most prominent writers-intellectuals of the time like Jorge Luis Borges, Silvina Ocampo, and Adolfo Bioy Casares to name just a few of the acquaintances he befriended, but perhaps the most influential. Wilcock would later refer to the three as a constellation and the Trinity, which helped him elevate from what he called a “grey existence”. In 1945 Wilcock undertook the self-publication of two collections of poetry: Ensayos de poesía lírica and Persecución de las musas menores. The following year he would again obtain the award granted by the Argentine Society of Writers (SADE) for his Paseo Sentimental. Also in 1946, Wilcock published his Los hermosos días.

At the time, General Juan Peron’s regime was suffocating intellectual life in Argentina; as World War II was over in Europe, many chose to relocate to the newly liberated capitals of the old world. In 1951 Wilcock left Argentina for the first time in a visit to Italy. He traveled in the company of Ocampo and Bioy Casares.

By 1953 he was residing in London earning a living as a translator and a commentator for the BBC. After a short return to Buenos Aires in 1954 he once again set sail for Italy where he would settle for good three years later. From now on most of his works, some of his most celebrated, would be written in Italian, a language he learned to command better than most native Romans. In 1975, Wilcock requested the Italian citizenship which was finally granted to him a year after his death, which occurred in his country cottage in Lubriano, Province of Viterbo, north to Rome, in March 1978.

Juan Rodolfo Wilcock is buried in the Protestant Cemetery, Rome located near the Porta San Paolo alongside the Pyramid of Cestius.

• Libro de poemas y canciones (1940)
• Ensayos de poesía lírica (1945)
• Persecución de las musas menores (1945)
• Paseo sentimental (1946)
• Los hermosos días (1946, 1998)
• Sexto (1953, 1999)
• Los traidores (in collaboration with Silvina Ocampo, 1956)
• El caos (1974)

Published posthumously

• Poemas (1980)
• La sinagoga de los iconoclastas (1981, translated into English as The Temple of Iconoclasts)
• El ingeniero (1996)
• El estereoscopio de los solitarios (1998)
• Hechos inquietantes (1998)
• El libro de los monstruos (1999)
• Los dos indios alegres (2001), yet published in Italian and reviewed by P.P.Pasolini during 1973
• El templo etrusco (2004)