A source told ESPN.com's Pierre LeBrun the five-year deal is worth $33 million.
Stastny, whose father, Peter, is a member of the hockey Hall of Fame and the second-leading scorer in Avalanche/Nordiques history, has registered 164 points in 164 NHL games.
"Paul has clearly established himself as one of the bright young stars emerging in our game today," general manager Francois Giguere said in a statement. "At a young age, he's demonstrated tremendous skill, vision and composure on the ice and is recognized as one of the most complete players in our league."
A second-round draft pick in 2005, Stastny scored 78 points in 2006-07, finishing second to Evgeni Malkin for the Calder Trophy honoring the league's top rookie. That year, he set an NHL rookie record by scoring points in 20 straight games.
Last season, Stastny led the Avalanche with 71 points in 66 games and was selected to play in his first All-Star Game.
He leads the Avs with 15 points in 16 games this season.
Stastny helped the University of Denver win a national championship in 2004-05 and won the WCHA scoring title a year later before going pro.
Pierre LeBrun covers the NHL for ESPN.com. Information from The Associated Press contributed to this report.