Karns, 21, went 4-5 and fanned 57 in 13 starts this season for Texas Tech University. Karns was originally selected by the Astros in the 10th round of the 2006 First-Year Player Draft, but he did not sign. He began his collegiate career at North Carolina State, then transferred to Texas Tech after his freshman season.
Karns is currently pitching in the Texas Collegiate League, where he is 4-0 with a 1.20 ERA.
With Monday's signing, the Nationals have now agreed to terms with 28 players from the 2009 First-Year Player Draft, including 13 of their top 15 picks.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.