Tuesday marks 20 years since McCann completed his takeover of a club that was close to going out of business after an unpopular board had clung on to power for too long.
The Canada-based Scot transformed the club on and off the park.
He devised a redevelopment of Celtic Park that made the stadium one of Europe's best arenas, and launched a share issue that was backed enthusiastically by fans and put the club on the road to the financial stability they enjoy now.
He also oversaw a major improvement on the park which helped Celtic stop Rangers from setting a new Scottish record of 10 consecutive titles.
McCann made a major profit when selling his shares at the end of his five-year plan but is viewed as a saviour among many Celtic fans, Mulgrew included, and his contribution will be marked by the club on Saturday when the Scottish Premiership leaders host Inverness.
"As a supporter myself I'm very thankful for what he did for this club," Mulgrew said.
"To think we were on the brink of liquidation... the job he did was massive.
"It maybe wasn't appreciated at the time by all the fans but now you realise what a job he has done."
Mulgrew was just turning eight when McCann took over but was aware of the impact he made.
However, he feels time has further boosted the reputation of the businessman, who was booed by many fans when he unfurled the league flag in 1998, amid controversy over the departure of title-winning boss Wim Jansen.
"I remember the stadium getting built," Mulgrew said. "Maybe I didn't appreciate it at the time but when you look back now you can't thank him enough.
"He has done as well for this club as any player has ever done.
"I'm sure all the fans that maybe booed him before realise what he has done. At the time I didn't know much about it but when you look back you realise how stupid that was."
Neil Lennon's side will hope to mark Saturday's occasion with a victory after losing the chance to finish the league season unbeaten when they went down 2-1 at Aberdeen on Tuesday.
"We didn't want to speak too much about it but it would have been nice," Mulgrew said. "Now we just need to focus on picking up as many points as we can.
"At a club like Celtic you need to bounce back. The fans want to win every game and they demand you give your all.
"The manager does as well, every day in training he is on us and it shows this season, with the unbeaten run."