The act of "wonderful sportsmanship" was widely applauded on social media.
"An amazing moment between two amazing triathletes on the home straight in Birmingham," said one fan on Twitter.
However, not everyone saw it as a heartwarming moment, with many disagreeing with the penalty call on Wilde.
"What a load of bull****. Award Wilde the gold he deserves," said one fan on Twitter.
Wilde could still yet end up with a gold medal after the New Zealand team launched an official protest on the his behalf.
Despite the 24-year-old Kiwi happily accepting the silver medal at Sutton Park, the outcome of that appeal could take up to 30 days to determine.
Yee will not be denied the victory he fairly earned but, if the Kiwis' protest is successful, a second gold medal may be awarded.
READ MORE: Confusion and controversy: How Kiwi triathlete could share gold after 'stitch up'
Wilde was understandably upset about the initial ruling around his penalty, and labelled the decision "bull****".
But he didn't take anything away from his friendly rival Yee, later saying "he absolutely deserves it".
"We're amazing mates behind the scenes and we're great rivals on the course. I do not want to take that medal away from him – he absolutely deserves it," Wilde said.
"When I crossed the line, I told everyone that there was nothing we could do now. But it sounds like we can try to do something. I don't know too much about it."