Asked if he felt the Capitals wanted him to return, Trotz said, "I'll leave that up to the Caps to answer that. I think absolutely. We just won a Cup together. I don't think that was an issue. It was more principle."
Washington reached the playoffs in each of his four seasons and finished first in the Metropolitan Division the past three.
"I'm happy for him," MacLellan said. "I think he got what he wanted, and that's a good opportunity for him. It's a good payday for him too. So it worked out good."
Trotz said he did extensive research on the Islanders and believes he is entering a good situation, especially if general manager Lou Lamoriello can get center John Tavares signed to a new contract. Tavares, the Islanders captain, is scheduled to become an unrestricted free agent July 1.
Trotz was 205-89-34 with the Capitals and won the Jack Adams Award as NHL coach of the year in 2015-16. He is fifth in NHL history with 762 wins, 20 behind former Islanders coach Al Arbour. Trotz was 557-479-100 with 60 ties with the Nashville Predators from 1998-2014.
The Capitals have not named a coach, but associate coach Todd Reirden has been reported to be the frontrunner. Washington is the only NHL team without a coach.
The Islanders first play the Capitals on Nov. 26 next season.
"Same as trading a player, players going other places," MacLellan said. "It's going to be the same kind of energy I think. ...
"It's so weird. It's awkward. It's weird. I don't know what to make of it. I don't know what we could do with it."
NHL.com senior writer Dan Rosen contributed to this report.