Allegri was appointed on Wednesday following the departure of Antonio Conte, who left Juve by mutual consent 24 hours earlier.
The 46-year-old takes over following a mixed spell with Milan, which saw him win the Serie A title in his first season in charge in 2010-11 before a downturn in fortunes.
However, he has now been given a chance to restore his reputation with a Juve team that will be looking to win a fourth straight Scudetto in 2014-15.
And, although he was surprised by the offer, the job represents an opportunity Allegri is eager to make the most of.
"For me it's an honour, it was a bolt from the blue when I was called yesterday to ask whether I was available to coach Juventus," Allegri said at a press conference on Wednesday.
"I understand the scepticism of the fans that have seen the coach change in a day.
"I will conquer them with respect and results. I am here to continue and to improve the winning streak."
"We have a duty to play a great tournament in Europe," he added. "The Champions League has a great charm and Juve certainly deserves to be at least one of the top eight.
"Conte has represented so much for Juve. This team has dominated in Italy but we must improve in the Champions League."
