Colorado also picks up a third-round selection in the 2020 draft, the team announced Tuesday.
Soderberg is coming off a season in which he scored a career-high 23 goals. The 33-year-old center spent the last four seasons with the Avalanche after being acquired on June 25, 2015.
Avalanche general manager Joe Sakic says the trade of Soderberg gives some young centers a chance at more ice time.
The 29-year-old Connauton played in 50 games with the Coyotes in 2018-19, finishing with a goal and seven assists. He's skated in 310 NHL games with Dallas, Columbus and Arizona.
More AP NHL: https://apnews.com/NHL and https://twitter.com/AP-Sports