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.
Shades of green
Rifle green was originally adopted by rifle regiments in the 18th century, including the famous 95th Rifles of the Napoleonic Wars. As the traditional role of riflemen was that of marksmen and skirmishers who attacked behind the cover of trees, a dark green uniform was adopted as an early form of camouflage, as opposed to the colorful uniforms worn by other soldiers of the period. The vegetable based dyes used during the 18th and early 19th centuries were not fast, frequently fading after exposure to the elements to lighter shades of green or even brown. While this had advantages in terms of reduced visibility on active service, it did not make for a smart appearance on the peace-time parade ground. Accordingly, the color of the rifleman's uniform was progressively darkened until it approached black. After 1890 the development of chemical dyes permitted the adoption of the stable shade of rifle green now worn. In the U.S. armed forces, the green beret may be worn only by soldiers awarded the Special Forces Tab, signifying they have been qualified as special forces soldiers. The special forces beret is officially designated "beret, man's, wool, rifle green, army shade 297". Previously, rifle green uniforms had been issued to Hiram Berdan's elite 1st and 2nd United States Sharpshooters during the American Civil War.