The Chiefs released Houston on March 10 after failing to find a trade partner for their four-time Pro Bowl linebacker. He had been due a $15.25 million base salary in 2019.
"Of course I would have liked to play my whole career in one place, but that's not neither here or there," Houston said. "That's over and done with. I'm here now. I'm excited to be a Colt and I'm going to make the best of this opportunity."
A source told Schefter that the Colts inquired about trading for former Chiefs linebacker Dee Ford but in the end decided to hold on to draft-pick compensation and instead turned their attention to Houston.
Houston, who turned 30 in January, joined the Chiefs as a third-round draft pick (70th overall) from Georgia in 2011. He quickly showed his pass-rush ability by getting three sacks in a game against the Bears as a rookie. He had 22 sacks in 2014, missing the NFL record by a half-sack.
Houston hasn't come close to that standard since. His best sack total in the past four seasons is 9.5 in 2017. Houston has 78.5 career sacks, fourth on the Chiefs' all-time list.
The Colts landed their best pass-rush threat since Robert Mathis had 19.5 sacks in 2013 in Houston. He'll help a defense that finished tied for 19th the NFL in sacks last season with 38 while not having a legitimate pass rusher.
"I have plenty in the tank," Houston said. "I think some people don't believe that. So it's more so of what I'm about to show the world and myself because I know what I'm capable of."
In 2015, Houston signed a six-year contract worth $101 million, making him at the time the highest-paid defensive player in NFL history.
Houston was more than just a pass-rusher for the Chiefs. He was an excellent all-around player who defended the run well. He was a first-team All-Pro selection in 2014. And now he's got a new team.
"It's been a different process," Houston said. "Something I wasn't use to. I just wanted to make sure I took my time and make sure I went to a team I felt like was the perfect fit for me, that I thought was the perfect fit and enjoyed being around. This is a great fit for me and my family."
ESPN's Adam Teicher contributed to this report.