Stastny has spent his entire career with the Avalanche after being picked in the second round of the 2005 draft.
He thrived under first-year coach Patrick Roy last season, scoring 25 goals as he helped the Avalanche overtake St. Louis for the Central Division crown and into the postseason for the first time since 2009-10.
The 28-year-old Stastny is a St. Louis native. His father, Hall of Famer Peter Stastny, and brother, Yan Stastny, are former Blues players. Paul and Peter Stastny will be the fifth father-son combination to have played for the Blues in franchise history.
AP Sports Writer John Wawrow contributed from Buffalo, New York.