Gibson was drafted by the Minnesota Twins with the 22nd overall pick of the 2009 Major League Baseball Draft. He was given a $1,800,000 signing bonus. Prior to the 2010 season, Gibson was rated the number 61 overall prospect by Baseball America. In 2010, he started the year with the class AFort Myers Miracle then was called up to the class AA New Britain Rock Cats. On August 13 Gibson was promoted to the class AAA Rochester Red Wings. Going into the 2011 season, Gibson was rated the number 34 overall prospect by Baseball America. Gibson was part of 19 non-roster players to get invited to spring training in 2011. Gibson spent the 2011 season with the Red Wings but after 18 starts, was sidelined with a sore elbow, ultimately resulting in his undergoing Tommy John surgery on November 7, 2011. Gibson returned in late 2012, starting two games for the Red Wings and six more in the Arizona Fall League. Gibson made his major league debut on June 29, 2013, against the Kansas City Royals. He pitched six innings, giving up two runs on eight hits, walking none and striking out five while also picking up his first major leaguewin. Gibson wound up with a 6.53 ERA in 10 starts for the Twins. For the 2014 season, Gibson was a mainstay in the Twins rotation, contributing 13 wins in 31 starts for Minnesota. His ERA was 4.47, second to Phil Hughes on the starting staff. The following year, Gibson improved his numbers overall from 2014. He led the team in innings, in wins and bettered his ERA from 4.47 to 3.84 in 2015. After suffering a right shoulder strain early in 2016, he remained a part of the Twins’ rotation but saw a dip in the quality of his numbers. Starting in 25 games that year, he had an ERA of 5.07 and batters hit over.290 against him. He compiled the same ERA in 2017, but with 12 wins, and hitters again hit over.290 against him. In 2018, he entered the Twins’ rotation again and started achieving a career-high strikeout rate than before — as of June 2018, he had struck out 66 batters in just 63 innings. Gibson finished the season with a record of 10-13 in innings. He led the team in ERA, finishing with a 3.62 ERA and a career high 179 strikeouts. He slotted 2nd in the Twins rotation in 2019. Gibson's K/9 rose to a career high 9 despite registering an ERA of 4.84 in 160 innings. Gibson tied a career high in wins with 13.
Texas Rangers
On December 6, 2019, Gibson signed a three-year contract with the Texas Rangers.
Scouting report
A groundball pitcher since his days in the minors, Gibson relies on a 92 MPH sinker, an 81 MPH curveball, an 85 MPH circle change-up and an 85 MPH slider.
Personal life
Gibson is married to Elizabeth Gibson. The married couple have three children together. Gibson is a Christian. Gibson was diagnosed with ulcerative colitis near the end of the 2019 season.