Quoting directly from Doug Murray's marvellous little publication "The Ninety-Nine: a History of the Savage Model 99 Rifle" in 'Part 4: The Cartridges'

'The .300 Savage' (page 4-16)

"In the early 1950's the .300 Savage round was modified by the Army to develop the 7.62 NATO cartridge design. In 1952 it was introduced to the civilian market as the .308 Winchester, and in 1954 was adopted by the Army as the 7.62 NATO round."