Baroni was axed after Torino lost at Genoa, marking their fourth straight winless match in all competitions. The club played the entire second half with 10 men and currently sits 15th in Serie A, just three points clear of the relegation zone.
The 50-year-old D'Aversa, an Italian born in Stuttgart, Germany, has signed a contract with Torino until June 30. The former Serie A midfielder has previously coached Italian sides including Empoli, Lecce, Sampdoria, Parma and Virtus Lanciano.