Janssen was born in 1931 in Naponee, a village in Franklin County in southern Nebraska, to Harold Edward Meyer, a banker (May 12, 1906 – November 4, 1990) and Berniece Graf (May 11, 1910 – November 26, 1995). Janssen was of Irish and Jewish descent. Following his parents' divorce in 1935, his mother moved with five-year-old David to Los Angeles, California, and later married Eugene Janssen (February 18, 1918 – March 30, 1996) in 1940 in Los Angeles. Young David used his stepfather's name after he entered show Business as a child.