After appearing at U20 level, Melli made his senior debut for Italy in March 2011 in an exhibition game against an Italian All-Star side but had to wait until EuroBasket 2013 for a first competitive outing. Previously he had played in European Championships at U16, U18 and U20 levels, helping the Italians to U20 silver in 2011. He made his first appearance for hometown club Reggio Emilia at the age of 16, before switching to Milano where he won the Italian scudetto in 2014. He is a supporter of Inter Milan football and is a keen cook. Melli is the son of volleyball player Julie Vollertsen, who won the silver medal with Team USA at the 1984 Olympic Games in Los Angeles, and Leopoldo Melli, who also played for Reggio Emilia. His younger brother Enrico is also a junior player at Reggio.