Born in Burano (an island of Venice), into a family of Musicians, Donaggio began studying violin at the age of ten, first at the Benedetto Marcello conservatory in Venice, followed by the Giuseppe Verdi Conservatory in Milan. At the age of 14, he made his solo debut in a Vivaldi concert for Italian radio, then went on to play for both the I Solisti Veneti and the Solisti di Milano. The discovery of rock and roll during the summer of 1959 ended Donaggio's classical career when he made his singing debut with Paul Anka. He then began to write his own songs and established himself as one of Italy's prominent singer-songwriters. He took part in the Sanremo Festival with "Come sinfonia" (1961) and had a string of successes including "Una casa in cima al mondo".
However, his greatest hit was the 1965 hit "Io che non vivo", which sold 80 million records worldwide and was performed most popularly in English as "You Don't Have to Say You Love Me" by Dusty Springfield and Elvis Presley.
In 2012 he was awarded the Lifetime Achievement Award from the World Soundtrack Academy.