The agreement was reached Friday, the first day Toronto's first-line centre could've signed with another team as an unrestricted free agent.
Bozak had 12 points and 28 points in the shortened season. He had career highs the previous year with 18 goals and 47 points. The 27-year-old Bozak has 53 goals and 134 assists in his four-year career.
Bozak, who is from Regina, Saskatchewan, helped the Original Six franchise reach the playoffs this year for the first time since 2004. He was scratched with an undisclosed injury in Game 7 of the first round against Boston when the Maple Leafs blew a three-goal, third-period lead and lost 5-4 in overtime.