Chievo have also announced the capture of Charleroi's French striker Cyril Thereau.
“Two new arrivals for the Gialloblu,” Chievo confirmed in a statement on the club website.
Andreolli was part of the Inter squad, but sold to Roma as part of a transfer swap without playing very regularly.
The defender is still only 24 years old and should finally get some first team football in Verona.
Thereau is 27 and comes from Belgian side Charleroi, though his career also includes a spell at Anderlecht.