Vesey was highly touted coming out of college, winning the Hobey Baker Award in 2016 as the NCAA's top player. He recorded 56 goals and 48 assists in 70 games across his final two seasons at Harvard.
His NCAA success hasn't translated to the pros, though. The 27-year-old has tallied 59 goals and 51 assists in 304 career NHL games with the New York Rangers and Buffalo Sabres.
Vesey set career highs with 17 goals and 35 points in 2018-19 with the Rangers, but plummeted to career lows in 2019-20 with the Sabres, notching nine goals and 20 points in 64 games.
At 6-foot-3 and 199 pounds, Vesey will bring some size to Toronto's forward group. There's an opening at left wing on the Leafs' depth chart after Andreas Johnsson was flipped to the New Jersey Devils on Saturday.