Under Conte, Juve won three successive Scudetti before he left the club at the end of last season.
Allegri arrived as successor to Conte - who took up the role of Italy national coach on Thursday - and Buffon firmly believes the new man at the helm can continue the good work of the previous incumbent.
"Although this team is the brainchild of Conte, I think that Allegri has been signed for his quality and experience, which means knowing how to handle a team like that," the goalkeeper told Tuttosport.
"Allegri brings forward ideas that are very innovative. And very nice.
"Conte won everything in Italy. Pulling everything out of us? Yes, this is true. And I think that we can do well with the fact that someone doing something different has come in.
"We will be able to win even with Allegri. I am convinced that he will do great things.
"But only if on the part of the players we are hungry again. And are available. And have the same will to win as the last few years. It is essential to everything, if we want to continue to do well."