Coyotes general manager Don Maloney announced the deal on Tuesday, but didn't disclose financial details.
The 19-year-old Lessio had 34 goals and 25 assists in 66 regular-season games last season for the Oshawa Generals of the OHL, and added three goals and two assists in six playoff games. He tied for the team lead in goals and was second in points.
Lessio also took part in last month's Canada-Russia Challenge, a four-game international tournament between junior teams. He scored a goal in Game 4 to help Canada win.