Turquoise has three substantially independent traditions, and they should not be merged into a single body of lore.
Egypt mined turquoise in the Sinai from the Old Kingdom onward, at Serabit el-Khadim and Wadi Maghareh, where the mining expeditions left inscriptions and a temple to Hathor, called the Lady of Turquoise. This is among the oldest documented organised gem mining anywhere, and the turquoise is found in Egyptian jewellery from the earliest dynasties.
Persia produced the finest material from the mines near Nishapur, worked for well over a thousand years, and the intense unveined blue of that source set the standard the word turquoise implies. Persian turquoise was traded across Asia and into Europe, and the horseman's practice of fixing turquoise to bridles as a guard against falls is attested across the Persian and Turkic world.
The American Southwest is a wholly separate tradition. Turquoise was mined and worked at Cerrillos in New Mexico and elsewhere long before European contact, traded into Mesoamerica, and is central to Puebloan, Navajo and Apache ritual and ornament, and to Aztec mosaic work. The silver-and-turquoise jewellery now universally identified with the region is a later development: Navajo silversmithing begins in the mid-nineteenth century, learned from Mexican smiths, and the combination with turquoise develops from there, expanding enormously with the tourist trade from the 1880s.
Turquoise is the December birthstone. On the 1912 list December was lapis lazuli; turquoise and zircon came in with the 1952 revision, tanzanite in 2002.