Born in Genoa, Giacobbe started his career in the early 1970s and got his first success in 1974, with the song "Signora mia", which entered the top-ten on the Italian hit parade. Foreign about a decade, he got several major hits, usually consisting in romantic ballads characterized by intimate and sometimes malicious tones. His song ""El Jardín Prohibido", the Spanish-language version of "Il giardino proibito", peaked on first place at the Spanish hit parade in 1976.
The same year, he entered the main competition at the Sanremo Music Festival, ranking third with the song "Gli occhi di tua madre".
The song reached the second place on the Italian hit parade. His last major hit was the 1982 song "Sarà la nostalgia".
From the mid-1980s he mainly devoted his career to live concerts and to initiatives of solidarity. In 2003 he ranked second at the Viña del March International Song Festival.