Born in New York City, he entered City College of New York, and graduated with a B.S. degree magna cum laude in 1935 at the age of 20, and was awarded the Kenyon Prize in Mathematics and Physics. He also received a Charles A. Coffin Foundation Fellowship from the General Electric Company, which enabled him to attend graduate school at Princeton University, where he earned his M.S. and Ph.D. degrees in 1938. He did his post-doctoral research at the University of Pennsylvania before joining Stanford University. Hofstadter taught at Stanford University from 1950 to 1985. In his last few years he became interested in astrophysics and applied his knowledge of scintillators to the design of the EGRET gamma ray telescope of the Compton Gamma Ray Observatory.

Hofstadter's Erdős number is 5. In 1942 he married Nancy Givan from Baltimore, and they had three children: Laura, Molly - who was disabled and not able to communicate, and Pulitzer Prize winner Douglas Hofstadter.

Stanford University has an annual lecture series named after Hofstadter, the Robert Hofstadter Memorial Lectures, which consists of two lectures each year, one oriented toward the general public and the other oriented toward scientists.