The terms of the contract were not disclosed.
"We are very pleased to sign Brendan to an entry-level contract," said Coyotes general manager Don Maloney. "Brendan is a strong skater with great size and skill. He had an impressive prospect development camp and we look forward to watching his development."
The 6-foot-2, 205-pound Perlini, who was selected 12th overall by Arizona in the 2014 draft, registered 34 goals and 37 assists in 58 games with the Ontario Hockey League's Niagara IceDogs in 2013-14.
He led the IceDogs in goals and finished second on the team in scoring. He was also named the most sportsmanlike player on the IceDogs last season.
The 18-year-old native of Sault Ste. Marie, Ont., helped Canada win bronze at the 2014 junior world championship, scoring three goals and adding one assist in the tournament.