Hudson will be part of a closer-by-committee situation while Sean Doolittle (knee) is on the 10-day injured list, Jamal Collier of MLB.com reports.
Hudson allowed three hits and no walks while striking out two across 1.1 innings to earn the save Tuesday against the Reds.
Hudson was traded from the Blue Jays to the Nationals on Wednesday in exchange for Kyle Johnston, Scott Mitchell of TSN.ca reports.
Hudson allowed one run on two hits and a walk in 1.1 innings against the Yankees on Saturday but escaped with his second save of the season. He struck out one batter.
Hudson allowed only one walk and struck out three across 1.1 innings to earn the save Wednesday against the Orioles.
Hudson (3-2) took the loss Friday against the Padres, allowing three runs (two earned) on a hit and a walk in one inning of relief.
Hudson gave up a run on two hits and struck out one across one inning Friday against the White Sox.
Hudson will be used as an opener Friday against the White Sox, Shi Davidi of Sportsnet.ca reports.
Hudson struck out one in two-thirds of an inning Monday to record his third hold of the season in a win over the Twins.
Hudson will sign a major-league deal with the Blue Jays on Sunday, Shi Davidi of Sportsnet.ca reports.