Rossi, born the son of an electrical engineer in Venice, Italy, was educated at the universities of Padua and Bologna. He first taught at the universities of Florence and Padua before emigrating to America in 1938. There he worked at Chicago and Cornell universities and in 1943 moved to Los Alamos to work on the development of the atom bomb. After World War II he was appointed, in 1946, to the chair of physics at the Massachusetts Institute of Technology where he remained until his retirement in 1970.

Rossi's main work was in the field of cosmic rays. These had first been detected by Victor Hess in 1911 but, by 1930, there was little agreement on their real nature; it was not even certain whether or not they were charged particles. To answer this question most physicists had been inconclusively searching for a variation in intensity with latitude.

Instead, in 1930 Rossi proposed an experimental arrangement that would search for any east–west asymmetry. Charged particles coming from outer space would be deflected by the Earth's magnetic field eastward if positively charged and westward if negatively charged. To detect them Rossi suggested that two or more Geiger counters be arranged pointing eastward with their centers arranged in a straight line. A similar arrangement should be set up pointing westward. Thus only particles coming from the direction along the axis of the counters would register simultaneously on both or all of them. In 1934 Rossi set up his counters in the mountains of Eritrea and found a 26% excess of particles traveling eastward, thus showing that the majority of cosmic-ray particles are positively charged.

Rossi was the author of several books, including Cosmic Rays (1964), which has been used by generations of physics students.