Santorelli spent last season with the Vancouver Canucks.
Kontiola will reportedly make $1.1 million.
Coupled with Tuesday's signing of Leo Komarov, the Leafs retooled at forward after letting Mason Raymond, Dave Bolland and Jay McClement leave in free agency. Komarov returned to Toronto after a year in Russia's Kontinental Hockey League.
Kontiola could be the Leafs' No. 3 center. Santorelli could also fill that role or replace McClement on the fourth line.
Santorell had 10 goals and 18 assists in 49 games for Vancouver before a shoulder injury derailed his season.
Kontiola spent the past five seasons in the KHL. Before that he played 12 games for the Chicago Blackhawks in the 2007-08 season, getting five assists.
He helped Finland win a bronze medal at the Sochi Olympics with five points in six games.