Donadoni, 52, penned a two-year deal with Bologna who are third from bottom with only six points from 10 games after losing 1-0 to Inter Milan on Tuesday.
Donadoni won the Champions League three times as a player with AC Milan and has already coached Napoli and Parma in the top flight as well as taking charge of the Italian national team from 2006-2008.
“Roberto Donadoni is the new coach of Bologna,” the club announced on its website. “He will take charge of his first training session tomorrow afternoon (Thursday).”
Rossi was the second top-flight coach to be sacked this season after Fabrizio Castori who had been in charge of rock-bottom Carpi.