Zaccardo, 31, has signed a three-and-a-half-year deal at the San Siro.
In addition to Mesbah, Rodney Strasser could also be heading to Parma from Milan.
"I am delighted and honoured to be in a so important club and I will do everything to make my contribution," Zaccardo told Milan Channel.
"I'm proud that Milan has interested in me. At age 31 I am here, after so many Serie A matches and I will give everything".
Parma general manager Pietro Leonardi later confirmed that Strasser could indeed also be coming in.
"We are finalizing the exchange between Zaccardo and Mesbah with AC," he said.
"Also could be included in the deal Strasser, the negotiations are well underway."