"I'm very, very happy and very motivated," the 60-year-old Lippi told the ANSA news agency.
Donadoni, who had little top-level coaching experience when he was appointed in 2006, never gained widespread support during his tenure. His two-year contract extension, signed on the eve of Euro '08, was conditional on Italy reaching the semifinals.
The Azzurri fell to Spain on penalty kicks in the quarterfinals.
"I'm sorry a penalty has determined this situation," the former MetroStars midfielder told La Gazzetta dello Sport. "In these two years my Italy team has done something positive. One match cannot wipe that out."
Despite its world title, Italy must still enter World Cup 2010 qualifying. It is entered in a group with Bulgaria, Ireland, Cyprus, Georgia and Montenegro.