The evolution probably began with Fran Tarkenton. He was fast and fairly accurate, one of the first true dual-threat quarterbacks, though without much size.
It continued with names like Roger Staubach and Detroit's Greg Landry. James Harris made the Pro Bowl in 1974 and remains one of the NFL's underrated pioneers—not only because he was the first black QB to start and win an NFL playoff game, but also because of his skill set.
Then there was John Elway. On and on the evolution went. QBs would get slightly faster, slightly stronger, slightly bigger, and eventually the throwing accuracy would catch up with the evolving prototype.