In 1959 Coppi attained an Italian doctoral degree at the Milan Polytechnic Institute and was subsequently a docent and research scientist at the Polytechnic Institute and the University of Milan. In 1961 he was a scientist at the Princeton Plasma Physics Laboratory. From 1964 to 1967 he was an assistant professor at the University of California, San Diego, from 1967 to 1969 at the Institute for Advanced Study, and from 1968 professor at the Massachusetts Institute of Technology. In the 1980s Coppi was a member of the science team in the Voyager 2 space probe.
Coppi works on theoretical plasma physics, space plasmas and magnetic fusion. At MIT he initiated the Alcator Program, which led to the Russian-American Ignitor program, that aims at building near Moscow a fusion reactor with Coppi as the principal investigator for the project. In addition Coppi is taking a leading role in the Frascati Torus Program in Italy.
In 1987 Coppi received the James Clerk Maxwell Prize in Plasma Physics and also the Award of Excellence in Plasma Physics from the American Physical Society. He is a member of American Academy of Arts and Sciences (since 1976) and the American Association for the Advancement of Science and a fellow of the American Physical Society. He received the American Dante Alighieri Prize, the Science Prize of the Italian government, the science and technology prize from Italgas, and the gold medal of the Milan Polytechnic Institute. He was knighted Great Officer of the Order of Merit of the Republic of Italy.