All three players in the deal are former first-round draft picks.
Schmaltz, 22, was selected 20th overall by Chicago in 2014 and has two goals and nine assists in 23 games this season.
"Nick is a dynamic forward with top-line potential," said John Chayka, Arizona's head of hockey operations. "We feel he can be a core player of our team now and into the future. He's a good complement to our evolving forward group and a rare combination of speed, skill and creativity."
Strome, 21, the third overall pick in 2015, had three goals and three assists in 19 games for Arizona this season.
Perlini, 22, had two goals and four assists in 22 games for the Coyotes. He was the 12th overall pick in 2014.