Carter was the only arbitration-eligible player Houston did not offer a contract. The Astros offered them to American League Cy Young winner Dallas Keuchel, catcher Jason Castro, reliever Josh Fields, designated hitter Evan Gattis, and infielders Luis Valbuena and Marwin Gonzalez.
Houston also traded backup catcher Hank Conger to Tampa Bay for cash. He hit .229 with 11 homers and 33 RBIs in 73 games last season after being acquired in an offseason trade with the Angels.
Carter, who hit .199 with 24 homers and 64 RBIs this season, made $4,175,000 in 2015 in his first year of arbitration and likely would have gotten at least $5 million next year.
"It's a business decision," Carter said. "There are few guys in my position and guys coming up behind me, and I was making the most money, so I ended up being the odd man out."
Carter had a tough time this season. He was benched in the summer before working his way back into the lineup and hitting .344 in September to help the Astros earn the second AL wild-card spot, their first postseason berth since 2005.
"There's no hard feelings," Carter said. "I had a great time in Houston. I enjoyed watching the team grow and being a part of the turnaround."
The streaky hitter tied for second in the majors with 37 homers in 2014 and had 90 homers in just three seasons with the Astros after a trade from Oakland. He led the team in both homers and RBIs in 2013 when he had 29 homers and 82 RBIs, and 2014 when he had 88 RBIs to go with his 37 homers.
The 28-year-old is a career .217 hitter with 109 homers and 280 RBIs.
"I'm looking forward to finding a new team and being in a situation where I can pick and choose where I go," he said.