Federer claimed a record-equalling fifth title at the event with a 6-4 7-5 victory in the decider on Monday (AEDT).
The win saw Federer make it 20 victories from 23 meetings against his friend and fellow Swiss.
Wawrinka, a three-time grand-slam champion, was in tears during the trophy presentation, much to Federer's amusement.
"I would like to congratulate Roger. He's laughing, he's an a******, but it's OK," Warwinka said. "I lost some tough ones against you, but when you played the final in Australia, I was still your biggest fan, so congrats for your comeback and congrats for today.
"Congrats to your team, to your family and everybody who's been around you for many years.
"Anybody who loves tennis loves to watch you so it's always good to see you back at that level and hopefully for many years."
The result saw Federer continue his stunning comeback from a knee injury, adding an ATP 1000 title to his 18th major trophy – secured at the Australian Open – to begin 2017.
Federer, 35, was predictably thrilled with his 90th ATP World Tour title, and hopeful he can continue his form.
"It's been just a fairytale week once again. I'm still on the comeback. I hope my body is going to allow me to keep on playing," he said.
"I was very sad when I couldn't come here last year. Just being here is a beautiful feeling. It's one of my favourite tournaments.
"I came here for the first time 17 years ago. So to be here again as the champion is an amazing feeling."