And the Bell Centre crowd showed it again on Thursday night with a standing ovation in a 30-minute pre-game tribute to the former Canadiens captain ahead of a game against the Anaheim Ducks.
The nearly five-minute ovation brought tears to the 40-year-old Koivu, who retired after spending the last five years of his 18-year NHL career in Anaheim.
"I always felt that I was respected as a player and for the way I played the game, but what makes me feel humble was the way I was loved by the fans," Koivu said before the tribute. "Sometimes you think about why it happened, why they took me as their own.
"You can't explain it, but there has been a real, unique bond between the fans in Montreal and myself. They've shown their passion and love and support throughout the years and really, it's been amazing."
The ceremony began with a scoreboard montage of photos and a mix of mostly fans and former teammates thanking him and saluting his hockey career.
Koivu's wife Hanna, daughter Ilona and son Aatos, his father Jukka and mother Tuire were on the ice as he gave a moving 15-minute speech without the help of written notes.
"Bonjour mes amis de Montreal (hello my Montreal friends)," he began in French before switching to English to acknowledge another former captain, Jean Beliveau, who died Dec. 2 and who was the subject of a sombre pre-game ceremony only last week.
"He was the ultimate captain," Koivu told the crowd about Beliveau. "When I think of the great legends that were here before my time I feel honoured and privileged to have served as captain of the Canadiens for nine years. I consider that my greatest achievement."
The crowd roared when he said "Montreal truly is the most exciting place to play hockey," and "I will always be a Hab in my heart."
The night had been planned since before the season for the night the Ducks visited the Bell Centre.
He thanked every player, coach trainer and equipment man he worked with in Montreal. He thanked J.S.Tremblay, the former player and scout who convinced the Canadiens to draft him.
But he choked up thanking the team of doctors who saved his life when he was struck by abdominal cancer ahead of the 2001-02 season.
After being presented with a painting by the remaining Canadiens from his time in Montreal, he ended his speech in French, saying he will love the Montreal fans forever.
Koivu, a gifted centre from Finland, lived through soaring highs and terrible lows in his 13 seasons with the Canadiens from 1995 to 2009.
Never moreso than in 2001-02, when he was diagnosed with abdominal cancer at the start of training camp. After a season of debilitating treatments, he shocked the hockey world by returning with three games left in the regular season.
At his first game back, fans stood and cheered for several minutes.
Then Koivu helped the Canadiens make the playoffs as the eighth and final seed, and knock off the first-place Boston Bruins in the first round.
"That year, the lows I went through and then being able to come back and be a factor in the series, it was a dream come true," he told reporters earlier in the day. "It's like the whole story was written before.
"I don't want to use the word regret, but probably the only thing (missing), and I'm not only even talking about winning a Stanley Cup, is really, genuinely competing and maybe being in the finals. Because we saw that a few times, winning in the first and second round, how this city reacts when you win. That year was special."
The following season, Koivu had his best campaign with 71 points, but what won the fans over even more was how he started a foundation to raise $7 million for a PET scan machine to help in cancer diagnosis for others.
The story of Koivu's career was great talent but terrible luck.
Koivu was selected 21st overall in the 1993 draft and looked to be a scoring star in the making until his career was slowed by a series of knee and shoulder injuries. He was named captain in 1998, a job he held for 10 years.
He joined the Canadiens in 1995, just in time to see the storied franchise come apart with the replacement of general manager Serge Savard and coach Jacques Demers with the inexperienced Rejean Houle and Mario Tremblay.
Three months later, star goalie Patrick Roy was traded to Colorado and the team went into a downward spiral that took years to stop.
"That first few months, and then having the last game at the Forum and first game at the Bell Centre, I pretty much saw everything that can happen all in that first year," said Koivu. "And I realized fairly quickly how big hockey is in this city and this province.
"There were a tough few years not making the playoffs, but in the early 2000s, I think everybody saw a complete change and turnaround. Winning the Eastern Conference one year and having talented players coming up pretty much every year. It made a difference. I think the franchise is on that path now and their future is really bright.
"It was frustrating and hard but at the same time I'm really happy I stayed here and I was able to see the other side as well, a successful team."
Another scary moment followed in the 2006 playoffs, when he was high-sticked by Carolina's Justin Williams and suffered damage to his left eye.
The setbacks, and the grace and determination with which he fought back and handled them, had much to do with the affection fans developed for the first European ever to wear the C for the Canadiens.
On his first game at the Bell Centre as an Anaheim Duck in 2011, he got another long ovation instead of the boos departed Habs often get on their return.
"I really didn't know what to expect because I'd seen some former players that played somewhere else come here and the reception wasn't always as good," he said. "It was a pleasant surprise.
"It was like coming home, and when I got the reaction from the fans, I really felt the love and respect."
After the 2008-09 season, the Koivu family decided they needed a change. He signed a one-year deal as a free agent with Anaheim and ended up staying for five. It gave him a chance to play for a contender, even if the Ducks fell short of winning a Cup.
He ended his career with 255 goals and 832 points in 1,124 games.
He also played in four Olympics for Finland, winning a silver and three bronze medals. And he led Finland to silver at the 2004 World Cup of Hockey.
He and his family haven't decided whether to stay in California or return to Finland. He expects to stay in hockey in some capacity, coaching perhaps, but hasn't worked that out yet either.
For now, he's getting used to being a retired player, while acting as assistant coach of Aato's team.
"I haven't lost the passion for the game," he said. "I just didn't have that push, mentally, any more to play and compete and that's why I retired. But I wish that one day I'll still be part of it, in a significant role, somewhere in hockey."