Boone was born in Los Angeles, California, the middle child of Cecile (née Beckerman) and Kirk E. Boone, a well-to-do corporate lawyer. He was descended from Squire Boone, younger brother of frontiersman Daniel Boone. Richard's nephew is actor Randy Boone (born 1942); his cousin is actor-singer Pat Boone; his first cousin once removed is actress-singer Debby Boone (Pat's daughter). Boone graduated from Hoover High School in Glendale, California. He attended Stanford University in Palo Alto, California, but left prior to graduation and tried his hand at oil-rigging, bartending, painting and writing before joining the United States Navy in 1941. He served on three ships in the Pacific during World War II, seeing combat as an aviation ordnanceman and gunner on TBM Avenger torpedo planes.
After cancellation of his weekly show, Boone and his family moved to Honolulu, Hawaii. While living on Oahu, Boone helped persuade Leonard Freeman to film Hawaii Five-O exclusively in Hawaii. Prior to that, Freeman had planned to do "establishing" location shots in Hawaii, but to do most production in Southern California. Boone and others convinced Freeman that the islands could offer all necessary support for a major TV series and would provide an authenticity otherwise unobtainable. Freeman, impressed by Boone's love of Hawaii, offered him the role of Steve McGarrett; however, Boone turned it down, and the role went to Jack Lord, who shared Boone's enthusiasm, which Freeman considered vital. Coincidentally, Jack Lord had appeared with Boone in the first episode of Have Gun – Will Travel, entitled "Three Bells to Perdido."