Born in Terre Haute, Indiana, Peters was educated at Evansville College and the Massachusetts Institute of Technology. He then became Wright's first apprentice, joining the Taliesin Fellowship in 1932. In 1935 he married Wright's adopted daughter, Svetlana (who died in an automobile accident in 1946, along with their son Daniel). Peters raised their other son, Brandoch, on his own; he was later briefly married to Svetlana Alliluyeva, with whom he had a daughter, Olga.
Among his accomplishments were assisting Wright in the construction of Fallingwater and the Johnson Wax administration building in Racine. Peters was responsible for the structural designs of the Guggenheim Museum and for the laboratory tower at Johnson Wax, among many other projects.
Peters served as Chairman of the Frank Lloyd Wright Foundation from 1985 to 1991. He died in Madison, Wisconsin.