Former world heavyweight champion and billionaire hand out free food to city's poor.
Their ambassadors include fellow Canadian Celine Dion, basketball legend Michael Jordan, former US president Bill Clinton and Pele.
Yank said: "We do this all over the world. We were in Glasgow last night and I thought 'Why aren't we feeding anyone in Glasgow?' "So here we are. We've been to 57 countries and will have fed one billion meals by January.
"We have never accepted a single donation, and feed anyone, no matter what colour or religion - anyone who needs it.
"I'd love to win a peace prize so I can give it to Ali before he dies, as he has been very sick recently.
"We've been friends for 50 years. Without him, we could never have done this because in certain countries they won't let you bring in food. But when kings or presidents meet Ali, they become kids - he opens so many doors.
"Now that this mission is on our index, they will receive food continuously from us. All we ask for is a thank you letter in return."
Gary Jacobs added: "The work Yank has done is unbelievable. He is an amazing person and it's just a pity there aren't more like him."
Mission user James Welsh, 53, has been homeless for 13 years. The ex-rifleman with the Royal Green Jackets said: "It was amazing to meet Evander and shake his hand.
"Hopefully, his visit will highlight the homeless situation and make the Government sit up and do something about it."
Unemployed single-parent James Moohan, 38, said: "My burroo money doesn't go very far with my child so the help we get at the centre goes a long way."
Mission chaplain Gus McKay was facing a possible shortage in funds this year before the visit. He said: "There has been an increase in the number of people coming through our doors in recent times for food parcels.
"We provide a drop-in centre for anyone who needs it, and to be given PS10,000 of food was a most welcome surprise and it will certainly keep us going for a while."
Timothy Lovat, of Edzell Property Management, who helped arrange the visit, added: "SK Boxing promotions were instrumental in helping pull this together at the last minute, and we extend an enormous thank you to Yank, Yvette, Evander and to everyone else who made the visit possible."
BIG HITTERS Yank and Ali have fought hunger for two decades