Anderson's deal is a two-way contract in the first two years and carries an annual cap hit of $750,000.
Toronto acquired Anderson in the trade that sent Andreas Johnsson to the New Jersey Devils earlier this offseason. New Jersey selected Anderson in the third round of the 2016 draft, and he's tallied 13 points in 52 career NHL games.
The 22-year-old has earned comparisons to Maple Leafs forward Zach Hyman.
"That's something I strive to be ... a guy that does things the right way, plays hard, he's in the right spots, doesn't take short cuts," Anderson told TSN's Mark Masters after the trade. "Definitely a player I would like to follow in the footsteps of."
Anderson may compete for a job with the Maple Leafs this upcoming season, but his two-way contract indicates he'll likely start the year with the AHL's Toronto Marlies.