D'Amico was born in Mesagne, Province of Brindisi, Italy, and later lived in Milan. He was hired as a part-time office executive for his first job. He met Versace in 1982 and eventually embarked on a long-term relationship that lasted 15 years, until Versace's murder in 1997. During that time, he worked as designer for the Versace Sport line. D'Amico now runs his own fashion design company.
Versace's will left D'Amico with a pension of 50 million lire a month for life (about €26,000) and the right to live in any of Versace's homes in Italy and the United States. However, since the properties that were left to D'Amico in Gianni's will actually belonged to the company, the homes belonged to his sister Donatella, brother Santo, and his niece, Allegra. After working out some agreements with lawyers, D'Amico obtained a fraction of the pension, and a restricted right to live in Gianni's properties. D'Amico's relations with the rest of the Versace family have not always been easy; Donatella Versace said in March 1999 that "My relationship with Antonio is exactly as it was when Gianni was alive. I respected him as the boyfriend of my brother, but I never liked him as a person. So the relationship stayed the same."