Donati departs for Bari
"I asked Celtic for the chance to return to Italy and I am very grateful for (them) granting me that wish," Donati told the Celtic website.
"The new manager at Celtic (Tony Mowbray) trusted me and respected me but my desire to return to Italy was too strong.
Donati arrived at Celtic in June 2007 on a four-year deal from AC Milan and made 54 appearances, scoring four goals.
He had joined Milan from Atalanta in 2001 for 10 million pounds but only played 17 times.
"I'll miss playing in Scotland. The league is more physical and the Italian league is obviously more technical," added the 28-year-old.
"But what I will miss most of all is the fantastic supporters and the atmosphere they create at games. We can learn a lot from them in Italy."