Cosmi replaces Rossi at Palermo
"Palermo announce that Serse Cosmi has been named coach," the Serie A club said in a statement without giving details on the length of his deal.
The Sicilians had been in the running for the Champions League places but a run of bad results has knocked them down to eighth spot.
Cosmi, who failed to help keep Livorno in Serie A last term, is famous for his flat cap and excitable behaviour during games but he will also need broad shoulders to deal with volatile Palermo president Maurizio Zamparini.
"He has ruined my Palermo. Rossi has destroyed this team," the club owner told reporters after Sunday's defeat, where Udinese were 5-0 up at halftime and Alexis Sanchez scored four goals.
Media reports have said Zamparini, who has threatened to sell the club several times, wants Giampiero Gasperini to take over next season after he was sacked by Genoa in November.
Coaches are not allowed to manage two top-flight teams in one season under Serie A rules.