The 24-year-old forward had 10 assists in 57 regular-season games and no points in one Stanley Cup Playoff game last season for the Dallas Stars, who bought out the final season of his two-year, $5.9 million contract (average annual value of $2.95 million) on June 30.
"Valeri is a big, young winger who adds depth to our roster and brings competition to our training camp," Avalanche general manager Joe Sakic said. "He brings NHL experience to our team and we are excited to have him with our organization."
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Nichushkin, who was selected by the Stars with the No. 10 pick in the 2013 NHL Draft, has 74 points (23 goals, 51 assists) in 223 regular-season games and three points (one goal, two assists) in 17 playoff games.
A native of Chelyabinsk, Russia, he played for CSKA Moscow in the Kontinental Hockey League from 2016-18 before rejoining the Stars.