The first delivery will take place on Friday afternoon, Dixon said.
"I spoke to Chris. He apologised ... he and I share a vision of giving people healthy food."
Social media users had earlier criticised Revive on the cafe's own Facebook page for going public over the donation issue.
Jess Etheridge wrote that she understood Revive "may have felt miffed" the Mission turned down their food, but asked why they didn't phone or walk to the nearby mission to question what was going on.
"It's sad, because this story reflects much more negatively on your business - a corporate shaming a charity ... I just hope you might realise the error of your ways & accept the Mission made an honest mistake.
"Treating the needy like they're ungrateful is kicking the homeless while they're down. Poor form."
However, others shared their support for the cafe.
Dixon said the issue had got people talking about healthy food and homelessness, and that was a good thing.
In retrospect they could have gone to the Mission to seek more information, but they also felt the message they received - that there food was no longer wanted - was clear, he said.