Born in San Cesario di Lecce, Province of Lecce, Pellè is from Monteroni di Lecce. He could have chosen ballroom dancing as his profession after becoming national under-12s champion in partnership with his sister Fabiana. He started playing for local club Lecce's youth teams; his father Roberto was a striker for Lecce in Serie C. Graziano won two "Campionato Primavera" titles and the 2002 "Coppa Italia Primavera". He made his Serie A debut on 11 January 2004 in 1–2 home defeat against Bologna, making a total of two appearances in the season.