Richter was born in Brooklyn and was raised in the Queens neighborhood of Far Rockaway. He graduated from Far Rockaway High School, a school that also produced fellow laureates Baruch Samuel Blumberg and Richard Feynman.
As a professor at Stanford University, Richter built a particle accelerator called SPEAR (Stanford Positron-Electron Asymmetric Ring) with the help of David Ritson and the support of the U.S. Atomic Energy Commission. With it he discovered a new subatomic particle he called a psi particle (now called a J/ψ particle).
Richter serves on the board of directors of Scientists and Engineers for America, an organization focused on promoting sound science in American government.