The deal is pending a physical, sources said.
In Philadelphia, Gibson was 14-14 in 43 appearances (42 starts) with a 5.06 ERA. He made two scoreless relief appearances in this year's playoffs as the Phillies reached the World Series for the first time since 2009.
The 35-year-old Gibson made his first All-Star appearance in 2021 prior to the Rangers-Phillies trade. He has an 89-91 record and a 4.52 ERA in 10 major league seasons with the Minnesota Twins, Rangers and Phillies.
The 6-foot-6 Gibson was selected by Minnesota in the first round of the 2009 amateur draft. He made his big league debut with the Twins in 2013.
He spent his first first seven seasons with Minnesota, going 67-68 with a 4.52 ERA in 193 games, including 188 starts. He had his best year in 2018, finishing with a career-low 3.62 ERA in a career-best 196⅔ innings.
The Associated Press contributed to this report.