Zenga was axed after their 1-1 draw against Catania.
Rossi has signed a contract that will keep him in charge at Palermo until June 2011.
A statement from the club on Monday read: “US Palermo announces it has appointed Delio Rossi as the coach of the first team.
“The coach has signed a contract until June 30, 2011, with an option for the club to extend the contract for a further campaign. Rossi will be unveiled to the media tomorrow morning.”