Chuck Garfien of NBC Sports Chicago first reported Eaton and Chicago were in agreement on Tuesday.
Eaton, 32, became a free agent on Oct. 28 after the Nats declined their 2021 team option. He hit .226 last season with four home runs and 17 RBI in 41 games. His .669 OPS was his lowest mark since 2013.
Eaton's best years have come in D.C., hitting a career-high .301 in 2018 before smacking a career-high 15 home runs in 2019. He also enjoyed a fantastic World Series performance against the Houston Astros, hitting .320 with a .993 OPS thanks in part to a pair of home runs.
He added six RBI and notably hit a two-RBI single to give the Nats a 6-2 lead and some breathing room against the Astros in the top of the ninth inning in Game 7 of their World Series-winning campaign.
Eaton also hit a solo home run off Astros ace Justin Verlander to knot Game 6 at two runs apiece in the top of the fifth inning. Washington eventually won 7-2.
The outfielder notably led the league in triples in 2014 and 2016 while with the White Sox. He stole 47 bases during his time on the South Side, as well.
Without Eaton, the Nats have a few options, but Michael A. Taylor stands as the most obvious in-house choice.
The seven-year MLB veteran played the second-most games in right field last year with 11. The 29-year-old struggled at the dish with a .196 batting average but did hit five home runs with 16 RBI in 99 plate appearances.
The Nats are set at the other two outfield spots with left fielder Juan Soto and center fielder Victor Robles. The team can also look toward a plentiful outfielder free-agent market, which includes the Astros' George Springer and Michael Brantley, the Atlanta Braves' Marcell Ozuna and the Los Angeles Dodgers' Joc Pederson.
Eaton will likely slot into right field for the White Sox after Nomar Mazara posted a .228/.295/.294 slash line in 42 games last season. The veteran outfielder also had a rough 2020, but he hit .289/.367/.423 in the previous six years combined.
Given the depth of talent already in Chicago's lineup, adding Eaton to the mix only solidifies the team's chances of returning to the playoffs after losing in the AL Wild Card Round to the Oakland Athletics.