Born in
Newark, New Jersey, United States, and he studied piano with Elizabeth Connelly, piano and musicianship with flautist/alto saxophonist Rudolph John Winthrop (1883–1959), himself a student of
Engelbert Humperdinck. He spent time studying at the
Paris Conservatory, In 1947-48 Finegan studied with
Stefan Wolpe in New York City, and lived in Europe from 1948-1950 where he studied with
Darius Milhaud and
Valérie Soudères, a pianist and composer who premiered Bartók's 3rd Piano Concerto in Paris. After returning to the United States, in 1952, Finegan and
Eddie Sauter (whom Finegan had met in 1939) formed an ensemble, the
Sauter-Finegan Orchestra, which remained active until 1957. His arrangement of "
Doodletown Fifers" was one of the Sauter-Finegan Orchestra's best-known originals. Following this collaboration, Finegan found work in
advertising, writing music for commercials. In the 1970s, he arranged for the
Glenn Miller Orchestra and
Mel Lewis's orchestra. He taught jazz at the
University of Bridgeport in the 1980s. He wrote arrangements for cornetist
Warren Vaché (with the Scottish String Ensemble) in 2004, and the vocal group
Chanticleer until his death in 2008. ==Compositions==