The Poland international arrived from Arsenal last summer.
Szczesny said: "That first day was incredible. I arrived here thinking this was his last or penultimate year. I told myself this was an experience that could happen once in a lifetime.
“I expected Buffon to be a great goalkeeper, but as a man he's simply incredible. A real leader of the team, friends with everyone. He is somebody everyone loves: he helps everybody. He's a great person.
“I don't even need to say what he's like as a goalkeeper, because everyone knows that. It's a fantastic life experience working with him and I hope it can continue for another year.
“Every day at Juventus, you realise that there is a different responsibility here. We have to win, we are obligated to win it all. Winning is normality here, so there is this responsibility to work even harder than everyone else. I think that's what took Juve to win all these trophies, as six titles in a row is extraordinary. I'd like us to get to 10!"