Law (2-1) picked up the win in Sunday's comeback victory over the Marlins, pitching two scoreless innings and allowing two hits. He struck out three without walking a batter.
The Nationals selected Law's contract from Triple-A Rochester on Tuesday, Andrew Golden of The Washington Post reports.
Law signed a minor-league contract with the Nationals on Wednesday and received an invitation to major-league spring training, Robert Murray of FanSided.com reports.
Law gave up two hits in a scoreless ninth inning Saturday to record his second save of the season in a 3-2 win over the Mets.
Law allowed one hit over 2.1 scoreless innings in Saturday's 7-3 loss to Washington.
The Reds reinstated Law (elbow) from the 15-day injured list Sunday.
Law (elbow) had his rehab assignment transferred Wednesday to Triple-A Louisville.
Law (elbow) began a rehab assignment with High-A Dayton on Sunday and struck out a batter over a perfect inning.
Law (elbow) threw a live bullpen session Wednesday, Charlie Goldsmith of The Cincinnati Enquirer reports.
Law has been diagnosed with a mild flexor mass strain and will rest for 10 days, Charlie Goldsmith of The Cincinnati Enquirer reports.