Cabrera and the Nationals reached a preliminary agreement one week earlier, contingent upon Cabrera proving his health. The 6-foot-7 right-hander underwent MRI exams on his throwing shoulder and elbow as part of his physical.
Cabrera went on the disabled list with the Baltimore Orioles in September after experiencing pain and tingling in his right elbow during a side session.
The Orioles, who called the injury a sprained elbow, declined to offer the pitcher a contract for 2009, making him a free agent.
Cabrera went 48-59 with a 5.05 ERA in 147 games over five seasons in Baltimore. He went 12-8 as a rookie in 2004 but has had four consecutive losing seasons since, including 8-10 with a 5.25 ERA in 30 starts this year.