The PGA announced Moody's death but didn't release details such as a cause of death.
Moody won the U.S. Open just 15 months after ending a 14-year career in the U.S. Army. It was his only tour victory although he won the U.S. Senior Open in 1989 and 10 other senior tour tournaments.
"He will always be remembered for winning the 1969 U.S. Open, the last player to win after being in local and sectional qualifying," said PGA Tour Commissioner Tim Finchem.
His Army career resulted in his nickname "Sarge."
"We are all going to miss 'Sarge' who was a patriot first and a professional golfer second," Finchem said. "He embodied a bit of golf's everyman whom we all could identify with, having risen from his Oklahoma roots as part (Choctaw Indian) and serving his country in a 14-year Army career."