Baugh, who was 94 and had numerous health issues, died at Fisher County Hospital in Rotan, David Baugh said.
Sammy Baugh was a member of the Pro Football Hall of Fame's inaugural class.
David Baugh said his father had battled Alzheimer's and dementia for several years. He had been ill recently with kidney problems, low blood pressure and double pneumonia.
"It wasn't the same Sam we all knew," his son told The Associated Press. "He just finally wore out."
Sammy Baugh was the last surviving member of the Pro Football Hall of Fame's inaugural class.
After starring at TCU, "Slingin' Sammy" Baugh played with the Redskins from 1937 to 1952.
"Sammy Baugh embodied all we aspire to at the Washington Redskins," Redskins owner Dan Snyder said. "He was a competitor in everything he did and a winner. He was one of the greatest to ever play the game of football, and one of the greatest the Redskins ever had. My thoughts and prayers are with his family tonight."