Rossi was born to a Jewish family in Venice, Italy. He was the eldest of three sons of Rino Rossi and Lina Minerbi. His father was an electrical engineer, who participated in the electrification of Venice. Rossi was tutored at home until the age of fourteen, after which he attended the Ginnasio and the Liceo in Venice. After beginning his university studies at the University of Padua, he undertook advanced work at the University of Bologna, where he received a Laurea in Physics in 1927. His thesis advisor was Quirino Majorana, who was a well-known experimentalist and an uncle of the physicist Ettore Majorana.