The Nationals will receive minor-league infielder Gilbert Lara and minor-league catcher KJ Harrison in exchange for Gonzalez, per USA Today's Bob Nightengale.
The move will bolster a Brewers staff that has been decimated by injuries to Brent Suter (Tommy John surgery) and Jimmy Nelson (shoulder surgery).
An 11-year veteran, Gonzalez is 7-11 with a 4.57 ERA and 1.53 WHIP this season. He's logged his highest walk rate per nine innings (4.3) since 2009.
He's been especially shaky since the All-Star break with a 6.55 ERA, 32 strikeouts and 22 walks across 44 innings.
But with few options ahead of Friday's waiver trade deadline, the Brewers couldn't be picky as they continue to pursue a National League playoff spot.