Zimmermann's deal is for US$2.3 million, Gorzelanny gets $3 million and Clippard $1.65 million.
Zimmermann, a right-hander, is expected to be Washington's No. 3 starter in 2012. Coming off right elbow surgery, he went 8-11 with a 3.18 earned-run average last season.
Clippard made the all-star team as a setup man last year, when the right-hander finished 3-0 with a 1.83 ERA in 72 appearances. Gorzelanny, a lefty, is slated for the bullpen this season.
Two players exchanged arbitration figures with the Nationals on Tuesday: pitcher John Lannan asked for $5.7 million and was offered $5 million, while outfielder Michael Morse requested $5 million and was offered $3.5 million.