Maddux, 54, is one of the most respected pitching coaches in baseball. He spent the past seven seasons as pitching coach of the Rangers, and he also held the same job with the Brewers from '03-08.
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"When we made the decision to hire Dusty, Mike became a free agent," Nationals general manager Mike Rizzo said. "After I talked to Dusty about it, he was the first guy we went after. We went after Mike extremely hard, aggressive and we got him. In one day he made his decision.
"[Maddux] is not only a mechanical expert, he is a mental skills expert. He really knows the ins and outs of pitching. He comes from a great pedigree. He's had great success and he has a great resume. He knows the art of pitching. He comes with a respect factor from the players that is hard to beat."
Under Maddux, Rangers pitchers helped the club reach the World Series in 2010 and '11. Texas' staff took the club as far as the American League Division Series this past season.
Maddux guided several All-Stars on the Rangers' starting staff, including Yu Darvish, Matt Harrison and C.J. Wilson, and also had a pair of closers -- Joe Nathan and Neftali Feliz -- earn All-Star selections.
During Maddux's seven years with the Rangers, his pitchers had a 4.06 ERA, good for sixth best in the AL. The Rangers' 3.83 ERA from 2010-13 was the third best among AL staffs.
According to MLB.com's T.R. Sullivan, the Rangers wanted Maddux to return next season, but he was given permission to consider other options.
"There was a period of time where Mike was looking around, and we did the same," Rangers general manager Jon Daniels told Sullivan. "As we talked internally, we did an internal review of what was best for the organization going forward. As we talked it through, we felt like there was an opportunity to get better with a new voice in that role."
In Milwaukee, Maddux guided Brewers staffs that featured All-Star starters Ben Sheets and Chris Capuano, and All-Star closers Francisco Cordero, Derrick Turnbow and Danny Kolb. The 2008 Brewers earned the National League Wild Card berth following the in-season acquisition of CC Sabathia, eventually losing in the NLDS.
Maddux most likely will have a starting staff that includes Stephen Strasburg, Max Scherzer and Gio Gonzalez in 2016. Those pitchers will hear a new voice in Maddux, whose preparation and work ethic are well-regarded.
Last season, the Nationals' pitching staff finished seventh in the Major Leagues with a 3.62 ERA.
Maddux, the brother of Hall of Fame pitcher Greg Maddux, was 39-37 with a 4.05 ERA in 472 career big league games (48 starts) over 15 seasons split between nine clubs.