The 26-year-old Gonzalez went 16-12 last season with a 3.12 earned-run average and 197 strikeouts in 202 innings pitched.
Gonzalez, a four-year veteran, has spent his entire big-league career with Oakland and has compiled a 38-32 record with a 3.93 earned-run average and 511 strikeouts in 535 innings pitched.
In exchange for Gonzalez, the Nationals dealt right-handed pitchers A.J. Cole and Brad Peacock, catcher Derek Norris and left-handed pitcher Tom Milone.
According to MLB.com, Peacock is the Nationals' No. 2 prospect behind Bryce Harper, with Cole third and Norris fifth.
Milone made five starts for the Nationals last season and went 1-0 with a 3.81 earned-run average and 15 strikeouts in 26 innings pitched.