Dozier was an All-Star in 2015 and won a Gold Glove in 2017, the last of a five-year stretch that saw him bat .252/.333/.465 with 145 home runs and 81 stolen bases while appearing in 767 games for the Minnesota Twins.
Dozier, 31, got off to a slow start in 2018, was traded to the Los Angeles Dodgers on July 31, struggled initially and hardly played down the stretch. The right-handed hitter finished the season with a .696 OPS, the lowest since his rookie year in 2012. Defensively, Dozier's minus-6.4 ultimate zone rating ranked 15th among 16 qualified second basemen.
He can still be an effective weapon against lefties, with a career .850 OPS against them.
During the 2016 and '17 seasons, Dozier finished in the top 13 in voting for the American League Most Valuable Player award.
Dozier's agreement with the Nationals could be the start of a number of free-agent infielders signing with teams. Among the players who could make moves soon are D.J. LeMahieu and Jed Lowrie. Also, sources told ESPN that the San Francisco Giants are floating Joe Panik in negotiations with other teams, adding the 2015 All-Star to the infield market.
ESPN's Alden Gonzalez contributed to this report.