González was originally signed by the Los Angeles Angels of Anaheim as an amateur free agent in 2005. The following two years, he earned a number of honors with the Arkansas Travelers.
After two seasons in the Red Sox minor league system, González signed a minor league deal with the Orioles in March 2012. He would start at Triple-A. He said that he signed to play with fellow Mexican players Dennys Reyes, Luis Ayala and Óscar Villarreal, as well as the fact that the Orioles gave him the opportunity to improve his skills. Gonzalez made his first major league start on July 6, 2012, against the Los Angeles Angels and earned the win, limiting the Angels to one run and three hits over seven innings. The Orioles won the game 3–2. In the game, González honored his former teammate Nick Adenhart, who died in 2009, by wearing a glove given to him by Adenhart when they were teammates in 2007 with the Arkansas Travelers. For the 2012 regular season he went 9–4 with a 3.25 ERA in 14 starts. González also started Game 3 of the 2012 American League Division Series against the New York Yankees, departing the game with a 2-1 lead but no-decisioned when the Yankees tied the game in the ninth inning and won it in the twelfth. On May 9, 2013, González was placed on the 15-day disabled list with an unhealed blister on his throwing thumb; at the time he had a record of 2-2 in six starts with an ERA of 4.58. González pitched in 30 games in 2013, making 28 starts. He pitched to a 3.78 ERA in 171 innings, striking out 120 batters. He earned a record of 11-8 on the year. On September 3, 2014, González pitched the first complete game and shutout of his career against the Cincinnati Reds. He finished the season with a 10-9 record in 27 games, pitching to an ERA 3.23 and WHIP of 1.30. He struck out 111 batters and pitched to a 122 ERA+. González made one start in the ALCS against the Royals, going 5 innings while allowing two runs. He took the loss in game 4, ultimately ending the Orioles season. González struck out a career-high 10 batters on April 14, 2015. González struggled with injuries throughout 2015, and finished with the worst year of his career. He went 9-12 in 26 starts and finished with a 4.91 ERA.
Chicago White Sox
On March 30, 2016, González received his unconditional release by the Orioles, who opted to cut him rather than send him to the minor leagues at the beginning of the 2016 season. In April 2016, González signed a minor league deal with the Chicago White Sox. González appeared in 24 games, 23 starts for the White Sox posting an ERA of 3.73. He finished with a record of 5-8. González began the 2017 season in the White Sox starting rotation. He spent a few weeks on the disabled list, limiting him to just 22 starts.
Texas Rangers
On August 31, 2017, the White Sox traded González to the Texas Rangers for infielder Ti'Quan Forbes. In 5 starts for the Rangers, González was 1-3 with a 6.45 ERA.
Return to the White Sox
González signed a one-year, $4.75 million contract with the White Sox on January 11, 2018. He appeared in 3 starts only before being lost for the season due to rotator cuff inflammation which required season-ending surgery. He elected free agency on October 29.
Pitching style
González throws five pitches: a four seam fastball at 92-93 MPH, a sinker at 91 mph, a curveball at 77-80, a slider at 84-86 and a splitter at 82-85 for his out pitch.
Personal life
González's wife, Lucía, gave birth to their first child, a daughter named Leah, in June 2013 in Southern California. Their second child, a son named Mateo, was born in August 2017.