Morrone was born on 3 October 1990 in Bitonto, Apulia. He is the youngest of four children, and he has three sisters. His mother, Angela, a seamstress, and his father, Natale, a construction worker, were both from Bitonto, but moved to Melegnano, Lombardy when their children were young in order to find better employment opportunities. His father died in 2003, when Morrone was 12 years old.
Morrone decided to become an actor after watching a Harry Potter film at age 11. He began acting in an after school program at his middle school. Morrone repeated his first year of high school after being held back for bad behavior. He then studied professional acting in a theater in the city of Pavia, at the Teatro Fraschini.