"[Hurricanes general manager Don Waddell] and I talked throughout the year occasionally," Brind'Amour said. "I thought we were on the same page, so it was just a matter of time. He knew I wanted to be a part of this, and I knew he wanted me to be a part of it too. So we figured it out.
"I would have a hard time thinking I could do the same job I'm doing here somewhere else. I've been here forever, and again, it's more about the people that I get to come to work with every day. That wouldn't be the case somewhere else. It just wouldn't be, so it's special to me. It just didn't enter my mind that I would leave, because with what we've got going on here, I want to see it through. We still have another level to get to and that's the mission."
The 50-year-old was named Hurricanes coach May 8, 2018, replacing Bill Peters, and is 120-66-20 in three seasons.
Also Thursday, Brind'Amour won the Jack Adams Award for NHL coach of the year as voted by members of the NHL Broadcasters' Association.
"He's done a tremendous job," Waddell said. "We truly believe we are headed in the right direction, so we're very happy to get Rod signed on a long-term deal and we look forward to the next steps."
Carolina was the No. 1 seed in the Discover Central Division this season and was eliminated in five games in the best-of-7 Stanley Cup Second Round by the Tampa Bay Lightning. The Hurricanes have qualified for the Stanley Cup Playoffs in each of Brind'Amour's seasons and advanced to the Eastern Conference Final in 2019, when they were swept by the Boston Bruins.
"We have a special group down here, and for me to do this job to the best of my ability, it's important to have the right people around me," Brind'Amour said. "I know what's down here. I know we have a great training staff, equipment people, the coaches. So that's why, I think, part of it took so long is a lot of people we had to figure out. We're at that point where we've pretty much done that."
Since Brind'Amour became coach, Carolina has won more games than all but the Lightning (141), Bruins (126), Washington Capitals (125), Vegas Golden Knights (122) and Pittsburgh Penguins (121).
"It was just a matter of coming to a deal from a financial end, and obviously [Hurricanes owner Tom Dundon] was very supportive of it and involved," Waddell said. "We talked early on that it was important to get the whole group done. From dealing with Rod, though, I have to put it on the easy side because of the relationship we have."
Brind'Amour played the final 10 of his 21 NHL seasons for the Hurricanes. He was captain when they won the Stanley Cup in 2006.
NHL.com staff writer Tracey Myers contributed to this report