The three-time All-Star posted the message Thursday on Twitter. He is eligible to sign with any other team.
Cole, 29, has been with the Astros since being traded from the Pittsburgh Pirates in January 2018. The seven-year veteran led the American League with a 2.50 ERA in 2019. He led Major League Baseball with 326 strikeouts.
"Last night [Wednesday] was a tough one for us and the heartbreak hasn't gotten any easier [Thursday]," Cole tweeted. "Before I became an Astro I didn't know much about Houston, but after just two years you have made it feel like home. So here's what I know now. You have been overwhelmingly friendly, welcoming, and kind to my family and me.
"The Astros organization has been such a pleasure to play for, the Cranes are indeed special people and great owners. I've met lifelong friends on the team and in the community and learned a little about pitching along the way."
Cole's fantastic season included winning his final 16 regular-season starts. His 326 punch-outs set a new franchise record. Cole is a frontrunner for the Cy Young Award, along with teammate Justin Verlander.
"This is a relationship between a team and it's fans like no other that I know," Cole said. "Thank you for making us better people and better players. This was a great season. We have a lot to be proud of."
Cole had a $13.5 million salary in 2019. The right-handed pitcher had a 1.72 ERA and a 4-1 record during the postseason. Cole logged a 3.86 ERA and a 1-1 record in two World Series appearances.