The Italian giants sacked Sarri after just one season despite winning Serie A following the club’s Champions League last-16 defeat by Lyon on Friday.
Pirlo, 41, has signed a two-year deal until June 2022.
The former Italy midfielder was only named the club’s Under-23 manager on 30 July.
Juventus said the decision to promote him is “based on the belief that Pirlo has what it takes to lead from his debut on the bench, an expert and talented squad to pursue new success”.
“The decision for Pirlo was very natural, in the Juventus style, because he is someone who played for us, has always been in contact with everyone here and it felt natural,” said Juventus’ chief football officer Fabio Paratici.
“We also believe he is pre-destined for greatness. He was as a player and we are confident he can do the same as a coach.”
Pirlo played 164 games for Juventus between 2011 and 2015 and won four Serie A titles in Turin after joining from AC Milan, with whom he spent most of his career and won two Champions League and two league titles.
Pirlo, who won 116 caps for Italy and helped them to win the 2006 World Cup, retired in 2017 having spent two years in Major League Soccer at New York City FC after leaving Juventus.
After he was appointed Under-23 boss, Pirlo said he would like to have the same “journey” as Manchester City boss Pep Guardiola and Real Madrid manager Zinedine Zidane.
Guardiola and Zidane coached Barcelona and Real Madrid’s reserve teams respectively before taking on the main job.
“But you need to earn it, gaining experience,” said Pirlo.
“The path I’m about to embark on is the right one for me.”
Pirlo played at Juventus alongside goalkeeper Gianluigi Buffon, who at 42 is older than his new boss.
Posting on Instagram after the announcement, Buffon wrote: “So now I have to call you Mister? Good luck #CoachPirlo.”
Former boss Sarri, 61, was appointed on a three-year contract last summer after one year at Premier League club Chelsea.
The Italian guided Juventus to a ninth straight Serie A title, although they lost three of their last four league matches to finish only a point clear of Inter Milan.
They were also beaten by Napoli in the Coppa Italia final after football in the country restarted following the coronavirus shutdown.
