Cole tweeted he was "excited to start this new chapter of my career in Denver."
Very excited to start this new chapter of my career in Denver with the @Avalanche. Looking forward to help build on this team's success. Huge thank you to everyone who helped me get to here - family, friends, and all my past teammates and organizations #GoAvsGo— Ian Cole (@ICole28) July 1, 2018
The two-time Stanley Cup champion in Pittsburgh didn't have the same postseason success in Columbus, as the Blue Jackets were eliminated in six games by the Washington Capitals. Cole had three assists in the series.
The Avalanche also added a second former Blue Jacket on Sunday when they signed forward Matt Calvert to a three-year contract. Calvert, 28, had 24 points for Columbus last season, tallying nine goals and 15 assists.
Between Pittsburgh and Columbus, Cole, 29, posted five goals and 15 assists with a plus-14 rating in 67 games during the regular season.
He has 97 points over eight seasons in the NHL, starting his career with the St. Louis Blues as a first-round pick in 2007.