A native of New York City, Moog attended the Bronx High School of Science in New York, graduating in 1952. Moog earned a bachelor's degree in physics from Queens College, New York in 1957, another in electrical engineering from Columbia University, and a Ph.D. in engineering physicsfrom Cornell University. Moog's awards include honorary doctorates from Polytechnic Institute of New York University (New York City) and Lycoming College (Williamsport, Pennsylvania)
During his lifetime, Moog founded two companies for manufacturing electronic musical instruments. He also worked as a consultant and vice president for new product research at Kurzweil Music Systems from 1984 to 1988, helping to develop the Kurzweil K2000. He spent the early 1990s as a research professor of music at the University of North Carolina at Asheville.
Moog received a Grammy Trustees Award for lifetime achievement in 1970. In 2002, Moog was honored with a Special Merit/Technical Grammy Award, and an honorary doctorate degree from Berklee College of Music.
He gave an enthusiastically-received lecture at the 2004 New Interfaces for Musical Expression (NIME-04), held in Hamamatsu, Japan's "City of Musical Instruments", in June, 2004. Moog was the inspiration behind the 2004 film Moog.
Moog's first wife was Shirleigh Moog (née Shirley May Leigh), a grammar school teacher whom he married in 1958. The couple had three daughters (Laura Moog Lanier, Michelle Moog-Koussa, Renee Moog) and one son (Matthew Moog) before their divorce. Moog was married to his second wife Ileana Grams, a philosophy professor, for nine years until his death. Moog's stepdaughter, Miranda Richmond, is Grams's daughter from a previous marriage. Moog also had five grandchildren.
Moog was diagnosed with a glioblastoma multiforme brain tumor on April 28, 2005. Nearly four months later, he died at the age of 71 in Asheville, North Carolina on August 21, 2005. The Bob Moog Foundation was created as a memorial, with the aim of continuing his life's work of developing electronic music.