Kopp was born in 1928 in Syracuse, New York. He graduated from Dartmouth College in 1949 and later from Harvard Law School. Kopp is married to the former Mara Sikaters and has three children: his eldest son, Shepard,
is a criminal defense attorney working in Los Angeles. His second son, Brad Kopp, is a musician who goes by the name Stark Raving Brad and lives in San Francisco. His daughter Jennifer is the executive director of the Napa Valley Grape Growers Association.