In 1933 Mompellio joined the faculty of the Palermo Conservatory as both a professor of music history and music librarian, but left after one year to become a professor of both music composition and music history as well as music librarian at the Parma Conservatory.[1][2] He remained in that position until 1938 when he was appointed librarian at the Milan Conservatory; serving in that position for the next eleven years.[2] He was largely responsible for saving the library's contents from destruction during World War II.[2]
In 1949 Mompellio's role at the Milan Conservatory changed from that of librarian to professor of music history; a position he remained in until 1968.[2] He also served as the vice-director of the conservatory for part of his later tenure at that institution.[2] He concurrently taught courses in music history part time at other universities during the first half of the 1950s, including the University of Milan, University of Florence, University of Pavia, and University of Parma.[2] In 1954 he joined the academic staff of the University of Parma and was made a full time professor there in 1968 when he left his position at the Milan Conservatory.[2]
From 1964 to 1968, Mompellio served as president of the Italian Society of Musicology.[2] He was also a member of the Accademia Nazionale di Santa Cecilia, and in 1983 he was the recipient of the Prix Antonio-Feltrinelli from the Accademia dei Lincei.[2]
As a scholar, Mompellio is best remembered for writing biographies on the composers Niccolò Paganini[1] and Sigismondo d'India.[2] He also authored several monographs on neglected Italian composers from the 15th through 19th centuries.[1] As a music editor he transcribed and reconstructed music written by Paganini and other historic Italian composers into contemporary music notation for the music publisher Casa Ricordi, including Paganini's Violin Concerto No. 5; a work discovered in 1972 long after the composer's death.[1] He also published several manuscripts of music by Paganini for which he served as music editor.[1] He wrote music criticism for Il diapason, Rivista italiana di musicologia, and Nuova Rivista musicale italiana among other periodicals.[1]
Federico Mompellio died in Domodossola on August 7, 1989.[2]