Donati, 43, has left his post as boss of Serie C side Legnano Salus to take over the Athens based club, who parted ways with former manager Alekos Vosniadis on Tuesday.
Kallithea are owned by American hedge fund manager Andrew Barroway, who used to own the now inactive NHL ice hockey team the Arizona Coyotes.
This season will mark the club’s first appearance in the top flight since the 2005/06 season, when they were known as Kallithea FC.
Donati spent the early stages of his playing career at Italian giants Atalanta.
After helping guide Atalanta to the top flight, he made the switch to AC Milan, where he would play 27 times under Fatih Terim, and legendary manager Carlo Ancelotti.
He would join Celtic in 2007, following a series of five loan spells, which stunted his development in Italy.
He made 31 league appearances for the Hoops before returning to Italy in 2009.
Donati would eventually return to Scotland, joining Hamilton Accies in 2016, where he appeared 41 times in the league for the Lanarkshire club.