Williams, who turns 48 on Nov. 28, was most recently was the third base coach for the Arizona Diamondbacks and was reportedly the top choice of Nationals General Manager Mike Rizzo.
Williams played third base and Rizzo was with Arizona's front office when the Diamondbacks won the 2001 World Series.
"I am thrilled to welcome Matt to our organization and am confident he is the best choice to lead the Nationals at this time," Rizzo said. "He is exceptionally prepared for the task. Matt came into the interview process already possessing an extensive knowledge of our organization: our roster, our minor league system -- and our fan base.
"He has genuinely creative, unique ideas on how to increase performance and on cultivating leadership and team unity."
Williams played 17 seasons in the major leagues and was on the Diamondbacks coaching staff the last four seasons. His only experience as a manager came last fall with Salt River in the Arizona Fall League.
In addition to winning a World Series in 2001, Williams was with the San Francisco Giants when they went to the World Series in 1989 and was on Cleveland's 1997 American League champion team.
He was selected to the All-Star team five times and won four Gold Gloves as a third baseman.
Williams replaces Johnson, who said after last season that 2013 would be his final year as manager. He is the team's fifth full-time manager since the franchise moved to Washington from Montreal in 2005.
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