Anderson was born in New York City, the son of Swedish immigrants. He studied physics and engineering at Caltech (B.S., 1927; Ph.D., 1930). Under the supervision of Robert A. Millikan, he began investigations into cosmic rays during the course of which he encountered unexpected particle tracks in his (modern versions now commonly referred to as an Anderson) cloud chamberphotographs that he correctly interpreted as having been created by a particle with the same mass as the electron, but with opposite electrical charge.
This discovery, announced in 1932 and later confirmed by others, validated Paul Dirac's theoretical prediction of the existence of the positron. Anderson first detected the particles in cosmic rays. He then produced more conclusive proof by shooting gamma rays produced by the natural radioactive nuclide ThC'' (208Tl) into other materials, resulting in the creation of positron-electron pairs. For this work, Anderson shared the 1936 Nobel Prize in Physics with Victor Hess.
Anderson spent all of his academic and research career at Caltech. During World War II, he conducted research in rocketry there. He was elected a Fellow of the American Academy of Arts and Sciences in 1950.