DeJesus, 33, has hit .250/.330/.401 with six homers in 318 plate appearances. He has spent time in center and left field for Chicago, and Fangraphs credits him with 1.8 wins above replacement.
It's unclear where the left-handed hitting DeJesus will fit into the Nationals lineup. Jayson Werth and Bryce Harper have both performed well this season in the corner outfield spots. Denard Span has been disappointing offensively, hitting .264/.314/.356 in 504 plate appearances, but is considered a better center fielder than DeJesus, and is also a left-handed hitter.
DeJesus is due around $1 million for the rest of the season, and the Nationals hold a club option for $6.5 million next year with a $1.5 million buyout. Harper, Werth and Span are all under team control in 2014.
The Nationals have had a disappointing season, entering Monday with a 60-63 record. Washington trails the Atlanta Braves by 15 1/2 games in the NL East, and sit 9 1/2 games out of the second NL wild card spot.