Phoenix took Gormley with the 13th overall selection and Visentin at No. 27 after trading down five spots in a deal with the Montreal Canadiens.
Gormley had nine goals and 34 assists in 58 games last season for Moncton of the Quebec Major Junior Hockey League. Gormley had two goals and 15 assists in 21 games in the playoffs as the Wildcats took the league title.
Phoenix had the 13th overall pick as part of March 2009 trade with Calgary. Coyotes general manager Don Maloney said he even thought about trading up to get Gormley.
"This was a very good pick," Maloney said. "I would say this was as good as we could ever expect."
Gromley said it didn't matter to him that he wasn't a top 10 pick.
"It's wasn't a big deal to me," he said. "Regardless of the number you get, it's what you do after the draft. There's a lot of work to be done and I couldn't be happier going to Phoenix."
Visentin had a 24-26-0-5 record in 55 games with Niagara of the Ontario Hockey League last season with a 2.99 goals-against average.
"I didn't expect to go in the first round at all," Visentin said. "I came (to Los Angeles) just to enjoy the experience and couldn't believe it. It was a pure shock to me."
Barring other trades, the Coyotes will have three picks in Saturday's final day of the seven-round draft being held at the Staples Center in Los Angeles. Phoenix has picks No. 52 and 57 overall in the second round and No. 138 overall in the fifth round.