Baroni was dismissed after Torino's fourth consecutive winless match in all competitions. The Granata played the entire second half with 10 men and currently sits 15th in Serie A, just three points above the relegation zone.
The 50-year-old D'Aversa, born in Stuttgart, Germany, has signed a contract until June 30. The former Serie A midfielder previously coached Italian sides Empoli, Lecce, Sampdoria, Parma, and Virtus Lanciano.