Terms were not announced, but sources told ESPN's Jim Bowden that Blanton will receive $4 million.
Blanton, 36, spent last season as one of the Los Angeles Dodgers' top relievers, going 7-2 with a 2.48 ERA. He helped stabilize the majors' busiest bullpen in 2016 with a .194 opponent batting average, 10th best in the National League. His 1.01 WHIP was 13th best in the NL.
The Dodgers' bullpen delivered franchise records in both innings pitched (590) and appearances (607) -- both numbers led the majors. Blanton's career-high 75 appearances led the way, tying for eighth in the NL, while his 2.48 ERA was 10th.
The heavy usage appeared to catch up with Blanton in the postseason, though, as he lost Game 1 of the NL Championship Series after giving up a grand slam to the Chicago Cubs' Miguel Montero and lost Game 5 when he allowed two runs in the sixth inning as the Cubs took the lead for good. Chicago clinched the series two days later.
The Nationals made room on the roster by designating catcher Spencer Kieboomfor assignment. The 25-year-old made his big league debut on the final day of the 2016 regular season, walking in his only plate appearance and scoring.
Fox Sports first reported the value of Blanton's deal.
ESPN Dodgers reporter Doug Padilla and The Associated Press contributed to this report.