He received bachelor's degrees in music and journalism from Syracuse University in 1976. He began freelancing as a critic and music feature writer for the Times in 1977, and joined the paper's staff in 1991. Before joining the Times, he was a contributing editor to High Fidelity and Keynote magazines, and a frequent contributor to Guitar Player, Keyboard, Pulse and other publications. He was also the first music critic for the New York Observer. Kozinn has written a number of books, including Guitar: The History, the Music, the Players (1984), Mischa Elman and the Romantic Style (1990), The Beatles (1995), Classical Music: A Critic's Guide to the 100 Most Important Recordings (2004).
He joined the faculty of New York University in 2004, and has taught courses in music criticism, Baroque music literature and the Beatles there. He also taught a course in the history of interpretation, as documented in a century of recordings, at the Juilliard School.