The D-backs also selected two players and added them to the 40-man roster.
Jaime, 23, missed the 2010 season following Tommy John surgery on his right elbow in April.
Jaime was 11-3 with a 2.43 ERA over parts of five seasons in the Nationals farm system. He was signed by the team as a non-drafted free agent on Dec. 7, 2004.
If healthy, Jaime could potentially be in the D-backs' bullpen plans for 2011.
Arizona also added right-handed pitcher Josh Collmenter and Yonata Ortega to the 40-man roster on Friday.
Collmenter, 24, combined to win 14 games last season after splitting the season between Class A Visalia, Double-A Mobile and Triple-A Reno. Over parts of four seasons in the D-backs organization, he is 40-27 record and 3.52 ERA.
Collmenter was selected by the D-backs in the 15th round of the 2007 First-Year Player Draft.
Ortega, 24, posted a 4-4 record with a 3.48 ERA in 48 games between Class A South Bend and Visalia this season. He led the organization with 33 total saves and was named to the Midwest League Postseason All-Star team.
Over parts of six seasons in the D-backs organization, Ortega is 6-16 record and 4.59 ERA. Ortega was signed by the D-backs as a non-drafted free agent on July 5, 2004.
The D-backs now have 39 players on their 40-man roster.