Kadri had 18 goals and 26 assists in 48 games during the lockout-shortened 2013 season.
The 22-year-old wanted a long-term contract from the Maple Leafs. Instead, Kadri and Toronto agreed to a so-called "bridge" deal that gives him another two years to prove his value.
The Montreal Canadiens' P.K. Subban missed the start of last season while trying to get a longer deal, but eventually settled for two years and $5.75 million. Subban won the Norris Trophy as the league's top defenseman.
Kadri's cap hit of $2.9 million will be higher than Subban's $2.875 million.
The Kadri signing leaves one major question for the Maple Leafs: the status of restricted free-agent defenseman Cody Franson, who remained unsigned as of Tuesday night. The 26-year-old Franson had four goals and 25 assists last season.
Training camp for the Leafs begins Wednesday.