That goes back at least to the 4th Century BC, often attributed to Alexander The Great.
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However, long before that, the Egyptians were shaving. They were said to be obsessed with hygiene and cleanliness. I'm pretty sure it goes back much further in prehistoric times.
On a mostly unrelated note, the NY Yankees have long maintained a similar policy for its players. Speculation has it that this was inspired by Steinbrenner's time in the Air Force.