The Nationals tallied an NL-best 96 wins and an NL East title in Williams' first season as a manager.
He was the only rookie manager up for the award in either league. Williams took over the Nationals before the season after Washington underperformed in 2013 and missed the postseason. He became the fourth manager to win in his first year.
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.
Williams received 18 first-place votes by the Baseball Writers' Association of America. The Pirates' Clint Hurdle, who won the award last year, was second with eight first-place votes. The Giants' Bruce Bochy was third, earning three first-place votes.
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."
Williams credited his players for the award, saying, "These guys made my transition easy."
Information from The Associated Press was used in this report.