CHICAGO -- The Chicago White Sox have agreed to terms on a one-year, $5-million contract with two-time All-Star left-handed pitcher Gio González, which includes a club option for 2021. Under terms of the agreement, González will receive $4.5 million in 2020, while the White Sox hold a $7-million option for 2021 with a $500,000 buyout.

González, 34, went 3-2 with a 3.50 ERA (34 ER/87.1 IP) and 78 strikeouts over 19 games (17 starts) with Milwaukee last season after signing as a free agent on April 27. He posted a 1.17 ERA (3 ER/23.0 IP) with 20 strikeouts in September.

“We view Gio as an important addition to our pitching staff,” said Rick Hahn, White Sox senior vice president/general manager. “He brings an impressive resume to our club as a veteran left-hander who has enjoyed success and should have a positive impact on our younger pitchers in terms of competing, battling and helping us win games at the major league level.”

 González, 6-foot and 205 pounds, is 130-99 with a 3.68 ERA (778 ER/1,901.1 IP) and 1,826 strikeouts in 332 games (324 starts) over 11 major-league seasons with Oakland (2008-11), Washington (2012-18) and Milwaukee (2018-19). He has recorded double digits in victories nine times during his career, has made 30-plus starts eight times, thrown 200.0-plus IP three times and posted 150-plus strikeouts eight times. González also has made eight postseason starts.

Among left-handers from 2010-18, González ranked among the major-league leaders in games started (2nd, 283), wins (4th, 120), opponents average (5th, .236), IP (5th, 1,681.1), strikeouts (6th, 1,605), quality starts (6th, 167) and ERA (8th, 3.49).

He ranked fifth in the NL with a 2.96 ERA in 2017 and was a finalist for the 2012 NL Cy Young Award after going 21-8 with a 2.87 ERA (64 ER/199.1 IP) and 207 strikeouts over 32 starts. González made the All-Star Team in consecutive seasons with Oakland in 2011 and the Nationals in 2012.

González, a native of Hialeah, Fla., orginally was selected by the White Sox in the first round (38th overall) of the 2004 First-Year Player Draft. He was traded to Philadelphia on November 25, 2005 with outfielder Aaron Rowand and pitcher Daniel Haigwood in exchange for Hall-of-Famer Jim Thome.

González was reacquired by the White Sox from the Phillies on December 7, 2006 with pitcher Gavin Floyd in return for pitcher Freddy García. He then was traded to Oakland on January 3, 2008 with pitcher Fautino De Los Santos and outfielder Ryan Sweeney in exchange for first baseman/outfielder Nick Swisher.

The White Sox 40-man roster increases to 39.