The terms of the deal have not been announced, but FIFA.com reports that Allegri has agreed to a two-year, €2 million ($2.7 million) deal with Juventus.
Allegri last managed at AC Milan, where he spent a little over three seasons before being sacked in January. Previously he had spent two seasons managing Cagliari.
Juventus won three consecutive Serie A league titles under Conte. During the 2013-14 season the club earned a record 102 points, becoming the first team in Italy to break the 100-point mark.
Allegri will be "unveiled" at a 3 p.m. CEST press conference on Wednesday as the new coach. Juventus club administrator Giuseppe Marotta will also take part.
- Sarah Barshop