Argento earned bachelor's and master's degrees from the Peabody Conservatory, where his teachers included Nicholas Nabokov, Henry Cowell, and Hugo Weisgall. Argento received his Ph.D. from the Eastman School of Music, where he studied with Alan Hovhaness and Howard Hanson. He also studied in Italy with Luigi Dallapiccola.

Argento has written thirteen operas. The majority of his music is vocal. In a predominantly tonal context, his music freely combines tonality, atonality and twelve-tone writing. Argento was awarded the Pulitzer Prize in 1975 for his song cycle "From the Diary of Virginia Woolf". Argento is a professor emeritus at the University of Minnesota.