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In page Salute:

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As early as 1745, a British order book stated that: "The men are ordered not to pull off their hats when they pass an officer, or to speak to them, but only to clap up their hands to their hats and bow as they pass." Over time, it became conventionalized into something resembling the modern hand salute.[3] In the Austrian Army the practice of making a hand salute replaced that of removing the headdress in 1790, although officers wearing cocked hats continued to remove them when greeting superiors until 1868.[4]