Berets of the United States Army
U.S. Army Special Forces wear the green beret because of their link to the British Commandos of World War II. The first Ranger unit, commonly known as Darby's Rangers, was formed in Northern Ireland during the summer of 1942. On completion of training at the Commando Training Depot at Achnacarry Castle in Scotland, those Rangers had the right to wear the British Commando green beret, but it was not part of the regulation uniform at the time and was disallowed by the U.S. Army. 
The 10th Special Forces Group (Airborne) had many veterans of World War II and Korea in its ranks when it was formed in 1952. Members of the 10th SFG began to unofficially wear a variety of berets while training, some favoring the red or maroon airborne beret, the black beret, or the green commando beret. In 1953, a beret whose design was based on that of the Canadian Army pattern, and which was rifle-green in color, was chosen for wear by Special Forces units.
Special Forces (United States Army)
In 1961, President John F. Kennedy authorized them for use exclusively by the U.S. Special Forces. Preparing for a 12 October visit to the Special Warfare Center at Fort Bragg, North Carolina, the President sent word to the Center's commander, Colonel William P. Yarborough, for all Special Forces soldiers to wear green berets as part of the event. The President felt that since they had a special mission, Special Forces should have something to set them apart from the rest. In 1962, he called the green beret "a symbol of excellence, a badge of courage, a mark of distinction in the fight for freedom".