Rodríguez was born in Mexico City, Mexico, the first son of the marriage of Pedro Natalio Rodríguez and Concepción "Conchita" Rodríguez (née de la Vega), and had three brothers, Federico, Ricardo and Alejandro, and a younger sister, Conchita.
He married Angelina (née Dammy), in Mexico since 1961, although he had a girlfriend in England, Glenda Foreman, with whom he lived in Bray on Thames in his latter years, but left no children.