Veteran free-agent left-hander Gio Gonzalez has agreed to a one-year, $5 million deal with the Chicago White Sox, a source confirmed to ESPN's Jeff Passan on Thursday.

Gonzalez will make $4.5 million in 2020 and is guaranteed $500,000 more if the $7 million team option for 2021 isn't picked up by Chicago, the source said.

Gonzalez was drafted by the White Sox with the 38th overall pick in the 2004 MLB draft, but was dealt to the Philadelphia Phillies in 2005 -- as the player to be named later -- in the deal that brought slugger Jim Thome to Chicago.

The 34-year-old Gonzalez was 3-2 with a 3.50 ERA and 78 strikeouts last season for the Milwaukee Brewers, who signed him to a one-year deal in late April. He made only six starts before spending more than a month on the injured list with left arm fatigue, recording a 2-1 record with a 3.19 ERA and 25 strikeouts. But he did return to make 11 more starts and log 56 1/3 innings in the second half as the Brewers won the wild card.

Gonzalez also spent the final month of the 2018 season with the Brewers, who acquired the two-time All-Star in an Aug. 31 trade with the Washington Nationals. He was 3-0 in five starts for the Brewers down the stretch, then started Games 1 and 4 of the NLCS against the Los Angeles Dodgers. He was pulled after two innings of the opener and one inning of his second appearance, allowing one run in each.

Gonzalez signed a minor league deal with the New York Yankees in mid-March last season but was released a month later after going 2-1 with a 6.00 ERA in three starts and 15 innings with Triple-A Scranton/Wilkes-Barre.

He was a career-best 21-8 in 2012, his first of six-plus seasons with the Nationals. After breaking into the majors with the Oakland Athletics in 2008, Gonzalez is 130-99 with a 3.68 ERA in 11 major league seasons and wrapped up the second option season of a contract last year that wound up being worth $65.5 million over seven years.