The 22-year-old moved to the Milan giants in January 2011, but has failed to break into the first team at San Siro.
With Samir Handanovic set to be first-choice keeper again this term, Bardi has opted to make the temporary move to the Stadio Marc'Antonio Bentegodi.
"I am very happy to be here, the feelings are very positive and I can't wait to settle in to the squad so I can get to work," Bardi told Chievo's official website.
"Chievo are the club who wanted me with the most conviction and I am very honoured by that, so I hope to repay their faith in me.
"I'm glad I will play with [striker] Alberto Paloschi. It makes me happy. With him, I've built a good friendship."
Bardi spent last season on loan with Livorno, but was unable to stop the club dropping into Serie B.
