Leivo, a six-foot-one, 173-pound left-winger, had 30 points (13 goals, 17 assists) in 64 games for the Ontario Hockey League club last season.
The No. 86 selection was Toronto's first pick on Day 2 of the draft at the Xcel Energy Centre. The Leafs sent their second-round pick (No. 39) and the No. 30 pick to Anaheim on Friday night for the Ducks' No. 22 selection.
Toronto used the pick to select American forward Tyler Biggs. The six-foot-two, 210-pounder spent last season with the U.S. under-18 national team development program. He had 28 points (17 goals, 11 assists) in 48 games.
His father, Don Biggs, was drafted in 1983 by Minnesota (156th overall) and played 11 games for Philadelphia in 1987.
The Leafs selected Mississauga-St. Michael's Majors defenceman Stuart Percy with the No. 25 pick.
The Oakville, Ont., native was named to the all-star team at the 2011 Memorial Cup, where the Majors lost to the Saint John Sea Dogs in the final. The six-foot, 186-pound blue-liner had 33 points (4-29) in 64 games last season.
A few hours before the start of the draft, Maple Leafs general manager Brian Burke acquired defenceman John-Michael Liles from Colorado for a second-round pick in 2012.
The Leafs selected defenceman Tom Nilsson from the Swedish junior league with the No. 100 pick and took Minnesota high school forward Tony Cameranesi at No. 130.
In the sixth round, the Leafs picked Sault Ste. Marie Greyhounds forward David Broll at No. 152 and added Brown University defenceman Dennis Robertson at No. 173.
Toronto selected a goaltender in the seventh round, taking Garret Sparks of the Guelph Storm at No. 190. The Leafs then took another Minnesota high schooler, defenceman Max Everson, with the 203rd pick.