The overhand throw is 1.8 million years old

Or at least it could be, based on anatomy. The NYTimes reports:

“You’re storing energy in your shoulder,” Dr. Roach said, speaking from Africa, where he was heading to Lake Turkana to look at fossil footprints of human ancestors about a million and a half years old. The storage occurs in the cocking motion, when a thrower brings hand and ball back, preparing to throw. “It works just like a slingshot would. You’re actually stretching the ligaments.”

Several developments in anatomy allowed humans to throw this way, he said, including a waist that allows twisting and a relatively open shoulder, compared with those of other primates like chimpanzees.

Looking at the fossil record, Dr. Roach and colleagues put the moment at which these changes came together in one body at about 1.8 million years ago, when Homo erectus first appeared. “It’s possible that Homo erectus could throw as fast as we do,” Dr. Roach said.

That's roughly when well-formed hand axes show up in the fossil record, though many of them are too large to be thrown. Crudely-formed stone tools are somewhat older (2.8 May).