"It's 99 percent done," Gonzalez said in a phone interview with The Associated Press. "It's pending a physical and I'm just waiting to hear from my agent."
The Nationals will also receive minor league right-hander Rob Gilliam from the A's, reported The Associated Press, citing a source with knowledge of the deal.
Gonzalez, who is 26 and in the first year of arbitration eligibility, is expected to command a salary of about $4 million for 2012.
Just before the Nationals deal was consummated, a Red Sox source told ESPNBoston.com he would be surprised if general manager Ben Cherington dealt for Gonzalez because he didn't believe Cherington would be willing to give up the organization's top prospects, which is what it would have taken to land the prized lefty.
The 26-year-old Gonzalez, drafted 38th overall by the Chicago White Sox in 2004, confirmed the trade to The Associated Press on Thursday. He went 16-12 last season -- a career high for wins after he earned 15 victories in 2010 -- with a 3.12 ERA in 32 starts and was selected to his first All-Star game. The left-hander has reached 200 innings the past two seasons.
"I love Oakland and appreciate them because they gave me a chance," Gonzalez said.
Gonzalez would give the Nationals the reliable starter they've been seeking for two years to go along with young arms Stephen Strasburg and Jordan Zimmermann. General manager Mike Rizzo made it a top priority last offseason to land another talented pitcher, and came through this time.
"I think we're an outfield bat away and a starting pitcher away from really being a contender in the division," he said late in the 2011 season.
Gonzalez was a big reason Oakland led the AL in ERA (3.56) and shutouts (17) in 2010 while holding opponents to a .245 batting average.
The Nationals went 80-81 this year to improve to third in the NL East after three straight last-place finishes in the five-team division.
A's general manager Billy Beane is in rebuilding mode, stockpiling talent in the farm system with the hopes of the franchise getting the go ahead to build a new ballpark some 40 miles south in San Jose despite the San Francisco Giants owning the territorial rights to technology-rich Santa Clara County. Beane and owner Lew Wolff have said they expect to hear soon from commissioner Bud Selig -- and Beane said the unsettled stadium situation would affect him being able to sign free agents this winter.
The A's (74-88) haven't posted a winning record or earned a playoff berth since being swept in the 2006 AL championship series by Detroit.
Beane also sent reliever Craig Breslow to the defending NL West champion Diamondbacks this month. That came after reliever Brad Ziegler was traded to Arizona in July. The A's appear to still be open to trading All-Star closer Andrew Bailey.
Peacock made his major league debut in September, pitching in three games with two starts -- winning them both -- to go 2-0 with a 0.75 ERA.
Milone also was a September call-up who made his debut in the big leagues. He went 1-0 with a 3.81 ERA in five starts. Milone was promoted after striking out 155 batters with just 16 walks this year at Triple-A Syracuse.
Norris has good power for a catcher. He hit 20 home runs for Double-A Harrisburg.
The 19-year-old Cole went 4-7 with a 4.04 ERA last season at Class-A Hagerstown.
Gilliam, the A's eighth-round pick in 2009, went 12-7 with a 5.04 ERA and 156 strikeouts for Class-A Vancouver this year.
Information from ESPN Insider Keith Law; ESPNBoston.com's Gordon Edes and Joe McDonald; and The Associated Press was used in this report.