The deal is worth $4.1 million, a source told ESPN's Pierre LeBrun.
The 24-year-old Kadri finished fourth among Maple Leafs players in scoring last season with 39 points (18 goals, 21 assists) in 73 regular-season games.
Kadri has appeared in 250 NHL games -- all with Toronto -- and has 152 points (64 goals, 88 assists).
He was selected by the Maple Leafs with the seventh overall pick of the 2009 draft.
The Associated Press contributed to this report.