The trio were technically free agents with the contracts at their former clubs having run out, although all three players were expected to join once the transfer window had opened and their previous deals expired.
|9/1||Inter are 9/1 with William Hill to win Serie A
Campagnaro, 33, has chosen to follow new Inter coach Walter Mazzarri - who replaced Andrea Stramaccioni as coach at the end of last season - from Napoli this summer.
Ex-Chievo defender Andreolli has put pen to paper on a four-year deal with the Nerazzurri, though the 27-year-old had been set to join the Serie A side since February.
In addition to the trio of free agents, Inter have signed up young attacking prospect Alessandro Capello, who is expected to be placed in the Primavera squad.