Jeffress was released by the Nationals on Sunday, Maria Torres of The Athletic reports.
Jeffress could be ready to pitch in spring games after a couple more batting practice sessions, Jessica Camerato of MLB.com reports. "Here's a guy that came to Spring Training, he's ready," Nationals manager Dave Martinez said Thursday. "The first time I saw him throw, he threw the ball really well. I asked him, 'Have you been throwing?' He said, 'Yeah, religiously.' He looks great."
Jeffress signed a minor-league contract with the Nationals on Monday, Mark Feinsand of MLB.com reports.
Jeffress worked around two walks to pitch a scoreless ninth inning and record the save in Friday's 1-0 win over the Twins.
Jeffress (4-1) allowed two earned runs on two walks and one hit to blow the save Tuesday against Cleveland. However, he did earn the win.
Jeffress earned the save against Cincinnati on Thursday, allowing one hit in a scoreless inning of work.
Jeffress (3-1) recorded the win in Tuesday's 8-7 victory over the Pirates in 11 innings, walking one and striking out two over 1.2 scoreless frames.
Jeffress logged 1.1 scoreless innings to record the save in Sunday's 2-1 win over the White Sox. He allowed a hit and two walks, while striking out one.
Jeffress pitched a scoreless seventh inning to record the save in Game 2 of Monday's doubleheader against the Cardinals.
Jeffress pitched 1.1 scoreless innings with a strikeout in Saturday's 4-3 win over the Pirates to record a hold.