The Flames will get a fourth-round choice in 2019 or 2020.
\[RELATED: 2017-18 NHL Trade Tracker\]
"I'm really excited," Hamonic said. "I have a pretty awesome opportunity in front of me. When my wife and I woke up and saw the news … we were kind of in limbo wondering if it happened or not, and then we found out and we're all pretty excited about going to Calgary, to say the least. That's an understatement. We're pretty jacked up."
Hamonic join a defense that also includes Mark Giordano, TJ Brodie and Dougie Hamilton.
"I think part of it is having the opportunity to play with those guys," Hamonic told the Flames website. "Those are three of the best defenseman in the League, in my opinion. When you have all three of them on one team and you get to join a defensive core with those kind of players ... I think that aspect really excites me."
Flames general manager Brad Treliving said he thinks Hamonic will fit in well on a team that earned the first wild card into the Stanley Cup Playoffs from the Western Conference but was swept by the Anaheim Ducks in the first round.
"He's certainly a guy that we've had our eye on for a while," Treliving said. "At the end of the day, you pay a price. You've got to give to get. You hate paying the price, but we look at a lot of things; we look at the makeup of our team, where he fits. He's a right shot, we think he fits in real good with our team. The coaches will figure out exactly where, but we had long talks. I think we can slide him in a Brodie situation. I like the looks of that top four.
"He moves pucks, he's a character kid, he's got some bite to him. I think he's going to fit good with us. It came together."
Hamonic, 27, had 14 points (three goals, 11 assists) in 49 games with the Islanders this season, averaging 20:27 of ice time. He had 108 blocked shots, ranking second on New York in blocks per game (2.2). Hamonic has three years remaining on a seven-year, $27 million contract with an average annual value of $3.86 million, according to CapFriendly.com.