The trade, which represents Washington's first major transaction of the offseason, comes one day after the Nats missed out on former White Sox ace Chris Sale, who had been strongly linked to the Nationals in trade talks but instead wound up going to the Boston Red Sox.
"It's never easy to let go of your prospects," Nationals general manager Mike Rizzo said. "You feel like a proud daddy when they get to the big leagues."
Eaton, who turned 28 years old on Tuesday, hit .284 with 14 home runs, 59 RBIs and an American League-leading nine triples. Eaton has a .284 career batting average with a .357 on-base percentage and a .414 slugging percentage, with 34 homers and 177 RBIs in five seasons in the majors. He led the AL in triples in two of the past three seasons.
"He's a high-energy guy," Rizzo said. "There's an edge to him."
Defensively, in his first season playing primarily right field, Eaton accounted for 22 runs saved, second-most in the AL behind Mookie Betts.
"We see the arrow still going up with him," Rizzo said.
A 19th-round pick of the Arizona Diamondbacks in 2010, Eaton has three guaranteed seasons left in a $23.5 million, five-year contract that calls for him to earn $4 million next year, $6 million in 2018 and $8.4 million in 2019. The deal includes a $9.5 million team option for 2020 with a $1.5 million buyout and, if 2020 is exercised, a 2021 team option for $10.5 million with a $1.5 million buyout.
"We discussed (Eaton) and several other players with the White Sox for quite a while now. It did gain momentum after the Sale deal was done," Rizzo said. "It actually came together fairly quickly over the last couple of days."
Predominantly a center fielder before last season, Eaton will likely switch back to center in Washington, a move that would allow young star Trea Turner to return to shortstop, his natural position.
"The only negative I've heard is you have to calm him down a little bit," Nationals manager Dusty Baker said of Eaton. "Because he goes 100 percent all the time, which is not a bad way to play this game. ... He's not afraid to get dirty and grimy, greasy, nasty -- do everything there is to beat you."
In the deal, the Nationals have surrendered two first-round picks. Giolito, the 16th overall selection in 2012, was rated as one of the top prospects in baseball this past summer by both ESPN's Keith Law (No. 2 overall) and Baseball America (No. 4 overall). In six games with Washington last season (four starts), the 6-foot-6 righty was 0-1 with a 6.75 ERA. Dunning, a University of Florida product, was the Nationals' first-round pick last season (29th overall).
Also headed to Chicago is Lopez, a 22-year-old native of the Dominican Republic who was rated as the team's third-best prospect. In 11 games with Washington in 2016, the 6-foot right-hander went 5-3 with a 4.91 ERA.
"We view all three of them, actually, as having the potential to become front-end-of-the-rotation pitchers," White Sox GM Rick Hahn said. "There's still a fair amount of development with each of them."
Information from ESPN's Eddie Matz and The Associated Press was used in this report.