Clippard, 22, made his Major League debut in 2007 and went 3-1 with a 6.33 ERA in six starts. Albaladejo also made his Major League debut this past season, giving up three runs in 14 1/3 innings out of the bullpen.
Nationals general manager Jim Bowden was not available for comment on the deal, which is pending physicals.
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.