Strome, who will turn 18 next month, was third in the OHL with 106 points (33 goals, 73 assists) in 65 games with the Niagara IceDogs. He was welcomed to the NHL when Minnesota native Kyle Okposo, an Islanders forward, made the pick from the podium in St. Paul.
Strome helped the IceDogs to a franchise-best 45 wins and 96 points last season when he posted a league-best 1.63 points per game among forwards.
The Mississauga, Ont., native, a six-foot, 175-pound centre, was chosen as the most improved player and best playmaker this season in a poll of coaches in the OHL's Eastern Conference.
"I love the colours and I think I'll fit in great there," Strome said. "I couldn't be happier right now.
"They're a young team. They've got a ton of assets. I want to grow with the team, and I want to win a championship. I know I'm young saying that, but that's what you want to do. You want to build from the ground up and that's what New York's doing, and I hope to contribute to that."
The Islanders have missed the playoffs in four straight years and five of six seasons. Strome will join a young core of forwards that features Okposo as well as Tavares, who was the 2009 No. 1 overall pick, fellow first-rounder Josh Bailey, and rookie of the year finalist Michael Grabner.
"We have set out a plan to build a young core of players that will consistently compete for the Stanley Cup, and Ryan is another key addition to that core," general manager Garth Snow said. "He is a highly skilled forward who's been very impressive in first two OHL seasons. Ryan's speed and creativity will help solidify our lineup for years to come."
Strome had to wait a moment as the Islanders were making the pick because he heard the name of his junior team being announced. He wasn't sure if they were calling him or his Niagara teammate, defenceman Dougie Hamilton, who went No. 9 to Boston.
"I saw Dougie Hamilton still on the board, so I wasn't sure," Strome said. "But I was just so thrilled. I really can't remember much of it. I have to watch the video when I'm done, but it was great. It was so fantastic."
Strome visited the Islanders before the NHL combine and put him through the rigours of a battery of tests before deciding they wanted to pick him.
"They did a psychological test," he said. "They came to Niagara, and I met with them another at the combine and went down to New York. I knew the interest was there, and I knew where they were selecting so it was a very good possibility. Things worked out.
"I got X-rays done, and MRIs of my body and a whole bunch of medicals done to make sure I'm healthy. I sat down and talked with them, and after they got to know me a little better, I think they wanted to do an extra background check."