The boonie hat was introduced to the United States Armed Forces during the Vietnam War, when U.S. Army Green Berets began wearing them in the field — rather than, well, berets:
These leopard spot or tigerstripe boonie hats were locally procured, the camo cloth was usually salvaged from other uniform items or with the former from a parachute or made up by the tailor. The name is derived from “boonie”, the abbreviated form of boondocks (itself originally American military slang derived from Tagalog bundok, “mountain”, during the Philippine-American War)