The 53-year-old Martinez agreed to a three-year contract, becoming the seventh manager in Nationals history since the club moved from Montreal before the 2005 season.
"We are delighted to bring Dave aboard and excited about what he will bring to our clubhouse and our dugout," owner Theodore Lerner said.
Martinez was considered the front-runner to replace Dusty Baker, who was fired as the Cubs manager last week after two seasons.
Martinez joins the Nationals for what will be his 30th season in American pro baseball. A 16-year major league outfielder, Martinez has been a coach for the last 10 seasons.
Martinez was a .276 career hitter while playing for nine different teams.