Allegri was a surprise appointment when he arrived at Juve last month following Antonio Conte's sudden resignation after leading the club to three straight Serie A titles.
Juve stalwart Buffon worked under Real Madrid boss Ancelotti when the duo were both at Parma and the goalkeeper believes Allegri possesses similar traits to the 55-year-old.
"Everyone has their own character," he told La Stampa. "There is no formula that guarantees victory, otherwise it would have been patented.
"There is the sergeant like Louis van Gaal and then there's those like Carlo Ancelotti, who look for direct contact, and they both know how to achieve success.
"Which style do I prefer? I was pleased with both approaches because I received an education that helped me to respect authority.
"It is up to the players to figure out how to interact with the coach so as to give their best. Ancelotti said that the coach must be one of the group, not above it. Allegri is like this and it is a quality that I like."
Juve may have dominated domestically in recent seasons but the Turin side have failed to take that form into the UEFA Champions League.
But Buffon is confident of changing that this season and pointed to the success of Borussia Dortmund and Atletico Madrid, who were finalists in 2012 and 2013 respectively, as inspiration.
"In the past two years Borussia Dortmund and Atletico Madrid have reached the final," he added. "Surprises do happen, although it is strange to define Juventus like this."
The 36-year-old also considered Juve's main contenders in the league for the upcoming season and believes Roma's success in the previous campaign marks them as the biggest threat.
"After last year they begin with enthusiasm and awareness of being competitive and having strengthened," Buffon continued. "At the start they are our equals."