Donadoni was sacked by Italy after an uninspiring showing at Euro 2008 and lasted just six months in charge of Napoli last year before being axed.
"I prefer to think about the future, I don't like looking back," the former Italy and AC Milan midfielder, who has signed a two-year contract, told a news conference.
"You learn from every mistake but you must also learn from every victory."
The Sardinians, in 17th place after only two wins this season, sacked Pierpaolo Bisoli on Monday after just 12 games in the job.
Former Cagliari player Bisoli, whose final game was Sunday's 1-0 home defeat by Genoa, was appointed in the close season after Massimiliano Allegri was released from his contract to join AC Milan.
Donadoni will take over a modest squad and has the added complication of not being able to pick Italy World Cup goalkeeper Federico Marchetti, who was dropped from the first team by president Massimo Cellino for asking for a transfer.
Marchetti, who has not played all season, has filed a case of unfair treatment against Cagliari and a league arbitration hearing is set for the end of the week.
Perennial mid-table team Cagliari recently unveiled ambitious plans to build a new stadium in the next two years to replace the decaying Sant'Elia.
