A native of New York City, Richter was born into a Jewish family in Brooklyn, and was raised in the Queens neighborhood of Far Rockaway. His parents were Fanny (Pollack) and Abraham Richter, a textile worker. He graduated from Far Rockaway High School, a school that also produced fellow laureates Baruch Samuel Blumberg and Richard Feynman. He attended Mercersburg Academy in Pennsylvania, then continued on to study at the Massachusetts Institute of Technology, where he received his bachelor's degree in 1952 and his PhD in 1956. He then joined the faculty of Stanford University, becoming a full professor in 1967. Richter was director of the Stanford Linear Accelerator Center (SLAC) from 1984 to 1999. He was a senior fellow of the Freeman Spogli Institute for International Studies and Paul Pigott Professor in the Physical Sciences Emeritus of Stanford University.