Reich was born in New York City to the Broadway lyricist June Sillman and Leonard Reich. When he was one year old, his parents divorced, and Reich divided his time between New York and California. He is the half-brother of writer Jonathan Carroll. He was given piano lessons as a child and describes growing up with the "middle-class favorites", having no exposure to music written before 1750 or after 1900. At the age of 14 he began to study music in earnest, after hearing music from the Baroque period and earlier, as well as music of the 20th century. Reich studied drums with Roland Kohloff in order to play jazz. While attending Cornell University, he minored in music and graduated in 1957 with a B.A. in Philosophy. Reich's B.A. thesis was on Ludwig Wittgenstein; later he would set texts by that philosopher to music in Proverb (1995) and You Are (variations) (2006).
For a year following graduation, Reich studied composition privately with Hall Overton before he enrolled at Juilliard to work with William Bergsma and Vincent Persichetti (1958–1961). Subsequently, he attended Mills College in Oakland, California, where he studied with Luciano Berio and Darius Milhaud (1961–1963) and earned a master's degree in composition. At Mills, Reich composed Melodica for melodica and tape, which appeared in 1986 on the three-LP release Music from Mills.
Reich worked with the San Francisco Tape Music Center along with Pauline Oliveros, Ramon Sender, Morton Subotnick, Phil Lesh and Terry Riley. He was involved with the premiere of Riley's In C and suggested the use of the eighth note pulse, which is now standard in performance of the piece.