Bennacer, a Algeria international, joined the Gunners in 2015 and played in the 3-0 League Cup loss to Sheffield Wednesday that year.
Baccaglini was named as Palermo's new president in March, but delays to the arrival of funds to complete a takeover saw Zamparini lose patience.
Statement on club's official website said Baccaglini and Zamparini met on Tuesday and closed the deal following a positive outcome of due diligence.
Parma have returned to Serie B after earning their second straight promotion on Saturday.
Benevento joined SPAL in ensuring there will be two new clubs in Serie A next season after they beat Carpi in a playoff on Thursday night.
Benevento won promotion to Serie A for the first time in their history on Monday after beating Carpi 1-0 in the second leg of their playoff final.