The Nationals tallied an NL-best 96 wins and an NL East title in Williams' first season as a manager.
He got 18 first-place votes and 109 points, joining Houston's Hal Lanier (1986), San Francisco's Dusty Baker (1993) and Florida's Joe Girardi (2006) as the only men to win in their first seasons as a major league manager.
"This is an organizational award as far as I'm concerned,'' Williams said on a conference call. "It's a testament to how the organization has built itself."
Pittsburgh's Clint Hurdle, who earned the NL honor last year, finished second to Williams with eight first-place votes and 80 points. Bruce Bochy of the World Series champion San Francisco Giants was third with three firsts and 30 points.
"For me, as a newcomer to the managerial fraternity, it is a privilege just to be considered amongst the best in our game. Clint and Bruce are certainly that," Williams said in a statement.
Williams took over the Nationals before the season after Washington underperformed in 2013 and missed the postseason.
The Nationals finished with a 17-game lead in the NL East, the largest of any division winner.
The Nationals overcame injury problems throughout the season, as five of the team's eight regulars landed on the disabled list at points during the year.
A hard-nosed player and five-time All-Star over 17 seasons, Williams was coaching third base for the Arizona when he was hired by Washington.
"Not having the experience of being there before, but you can rely on folks," he said.
Williams credited his players for the award, saying, "These guys made my transition easy."
The Pirates' Clint Hurdle, who won the award last year, was second in voting by the Baseball Writers' Association of America with eight first-place votes. The Giants' Bruce Bochy was third, earning three first-place votes.
Information from The Associated Press was used in this report.