Ben Davison, who trained Fury for two years but was ditched ahead of Sunday morning's clash, said the new WBC heavyweight belt-holder is a "national treasure".
"I truly believe that there should be a parade for Tyson," Davison said, not just because of his huge achievements in the ring, but because of "what he's done outside of the ropes as well".
Fury took two-and-a-half years out of the boxing ring while suffering with depression and addiction after he defeated another heavyweight champion - Wladimir Klitschko - back in 2015.
But he came back from the brink of suicide in his return to boxing and fans have commended his honesty in speaking about his mental health issues and subsequent recovery.
"He's inspired them and shown that he can come back and he can come back better than ever," Davison added.
Fury put in arguably the best performance of his career to beat Deontay Wilder by Technical Knock Out (TKO) in the seventh round.
After his first bout with Wilder in 2018, in which the pair drew, few could have imagined the mismatch that would follow in Sunday's fight, but Fury's former trainer Davison wasn't too surprised.
"We've seen Tyson put on masterclasses on the back-foot before, so we know that he's got that skill-set, he's able to do that."
He added: "We knew he had that skill-set, but to go and handle the highest and heaviest puncher in heavyweight history, that really says something."
But Davison doesn't think Fury's devastating win will silence all his critics.
"You'll never be able to silence all the doubters, but his name will be cemented among British boxing greats, if not the greatest, this country has ever seen," he said.
Looking ahead to the potential unification fight - where both opponents have the chance to win all world boxing's major belts - Davison said Fury will be "an impossible man to beat".
If the fight happens before either boxer loses any of their world heavyweight belts, the winner will become the first undisputed heavyweight champion of the four-belt era, which began in 2004.
"Tyson Fury is definitely one of - if the not the - greatest fighters to come out of this country," Davison said, "he's definitely up there with the all time greats of the heavyweights now and whatever he chooses to do with the rest of his career, he's cemented that".