Burakovsky, a 25-year-old forward who was a restricted free agent, had NHL career highs in goals (20), assists (25) and points (45) in 58 games with the Avalanche last season. He scored 17 points (seven goals, 10 assists) in 15 Stanley Cup Playoff games.
"Signing Andre was a priority for us this offseason," Avalanche general manager Joe Sakic said. "He has been a great addition to our team and was a big part of our success this season. He's a very skilled player who brings speed and scoring to our lineup, and we're excited to have him under contract for two more years."
Selected by the Washington Capitals in the first round of the 2013 NHL Draft, Burakovsky has 190 points (82 goals, 108 assists) 386 regular-season games with the Avalanche and Capitals and 35 points (16 goals, 19 assists) in 71 playoff games.
Burakovsky won the Stanley Cup with the Capitals in 2018.
Nichushkin, a 25-year-old forward who was a restricted free agent, scored 27 points (13 goals, 14 assists) in 65 games with the Avalanche last season and three points (two goals, one assist) in 15 postseason games.
"Valeri played important minutes for us this season and had one of the best years of his career," Avalanche general manager Joe Sakic said. "He is a big (6-foot-4, 210 pounds), young winger who provides depth scoring, can play up and down our lineup and is reliable defensively. We're happy to have him back for another two seasons."
Selected by the Dallas Stars in the first round (No. 10) of the 2013 NHL Draft, Nichushkin has scored 101 points (36 goals, 65 assists) in 288 NHL games.
Nichushkin, who returned to the NHL in 2018-19 after spending two seasons in the Kontinental Hockey League, has six points (three goals, three assists) in 32 NHL playoff games.