Trotz resigned from the Washington Capitals on Monday after coaching them to their first Stanley Cup championship since they entered the NHL in 1974. They defeated the Vegas Golden Knights in Game 5 of the Final on June 7.

"When you step down you take some chances," Trotz said. "I was obviously pleasantly surprised I got a call almost immediately once word got out in the inner circles. I said, 'I'm in, I want to listen.' ... [Islanders general manager Lou Lamoriello] told me about his vision and his plan for his team, what he's already done in a very short period of time, changing a lot of things, changing the culture and all that. I love that. That's what they hired me to do in Washington, change a little bit of the culture, try to win a Stanley Cup. So we're going to try and do the same thing on the Island."

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Terms of Trotz's contract were not released.

"He brings experience, he brings knowledge and he brings success, which is the most important thing," Lamoriello said. "You have to win. He knows how to win, and he's a good human being. So I think he's a great role model for what we're trying to do as far as bring to the organization."

The 55-year-old replaces Doug Weight, who was fired June 5. Lamoriello was hired as Islanders president May 22 and became GM when Garth Snow was fired along with Weight.

"I think that what we had said [was] we would try to get the best coach available, and when time is on your side, you use it," Lamoriello said. "We were in no rush. There were several people that we could've considered. When this transpired, I think it's obvious that we tried to do it as soon as we possibly could."

Trotz completed the final season of a four-year contract with Washington and resigned after the sides could not agree on an extension beyond the two years he received for winning the Stanley Cup.

"I went to the Caps and said, 'I think it's a little unfair based on value around the League,' and tell me if anything could be done," Trotz said. "When I got the response, I decided it was time to go in a different direction. I thanked them. They were nothing but first class. I said we were going to come there and win a Cup in four years ... we did that ... [it's] a special group and we are tied together.

"From a standpoint from myself in terms of principle, I took my chances and stepped down."

The Islanders were 35-37-10 in Weight's only full season, finishing 17 points behind the New Jersey Devils for the second wild card from the Eastern Conference. New York allowed 296 goals, most in the NHL, and a League high 35.6 shots-against per game.

"I think the strength of the core group is that they have a lot of skill," Trotz said. "They can play with pace. We've got to clean up our back end in terms of our defensive play without the puck. I know we can fix that, and get our goals-against down.

"This team is exciting. You look at John [Tavares] as a centerpiece, or a young guy like [Mathew] Barzal. You look at a number of guys like [Anders] Lee and [Jordan] Eberle … there's a lot of offense there. We've got some work to do, there is no question, but at the same time, there are some really good pieces there. If we can get our structure right, our pace right, we'll be able to score and we'll be able do defend much better. ... I've done my research on the GM and the organization, they are fully committed to making this a great franchise which it has been in the past and will again. ... I just want to be a part of it."

Video: NYI@DET: Tavares wins it in OT for Islanders

New York has not made the Stanley Cup Playoffs the past two seasons and has won one series since 1992-93 (against the Florida Panthers three seasons ago).

"I think what we need is, we need an individual who can walk in that locker room with the players who are there who have not really had a lot of success and he walks in there with instant success," Lamoriello said. "People follow that, and I think that that's a very important thing for these young men."

Tavares, the Islanders captain and No. 1 center, can become an unrestricted free agent July 1. He reportedly has been engaged in daily negotiations with New York and can begin to talk to other NHL teams on June 24.

"I think it's in good hands," Trotz said. "Lou has been in constant contact with John and has had great dialogue. Obviously I reached out to him as well and we had a great conversation. I think it's in good hands and I'll leave it between John and Lou. ... If you know anything about those two parties, they are of the highest integrity, both those gentleman. I think they'll have great dialogue and we're hopefully going to have John be a part of it for sure."

Trotz said he would like to have Capitals assistant Lane Lambert join him on his staff in New York.

"He's been asked if he can look around and has had permission," Trotz said of Lambert. "He'd be my No. 1 choice. I've talked to Lane and it's in his court."

Trotz was 205-89-34 with the Capitals and won the Jack Adams Award as NHL coach of the year in 2015-16. Washington reached the playoffs in each of his four seasons and finished first in the Metropolitan Division the past three.

"It's hard when it happened right away, you know?" Washington captain Alex Ovechkin said before Trotz was hired in New York. "First of all, thanks to him for being with us, to give us a chance to win the Cup. All of what he did was only for the team, not for personal-wise. But I'm pretty sure he will be fine and he will find what he wants."

The Capitals won the Presidents' Trophy in 2015-16 and 2016-17 but did not advance past the second round of the Stanley Cup Playoffs.

"It's tough," Washington forward Nicklas Backstrom said. "He's done a great job in our organization. I would say a little surprised, but at the same time, I understand him. But I think something you can't take away from Barry is what he's done to this team. Him and the coaching staff has been doing a tremendous job to just get us together. He's been schooling us good these four years and we got a good finish out of it."

Trotz is fifth in NHL history with 762 wins, 20 behind former Islanders coach Al Arbour for fourth place. Trotz was 557-479-100 with 60 ties during 15 seasons with the Nashville Predators from 1998-2014.

"I talked to the Capitals to make sure [they knew] I was very thankful for the opportunity," Trotz said. "We did something very special together, and my agent reached out to different people as this became public real quickly. I got the call from Lou and we met and we had a fantastic discussion. We made out a plan that he's trying to execute, and knowing him, he will execute, and it got me really excited."

Weight took over for Jack Capuano on Jan. 17, 2017 and coached the Islanders to a 24-12-4 finish last season to miss the playoffs by one point.

The Capitals are the only NHL team without a coach.

"It's good to be wanted," Trotz said. "It happened really quickly."

NHL.com staff writer David Satriano and columnist Nicholas J. Cotsonika contributed to this report.