The 27-year-old Slovenia international moved to San Siro from Genoa last August.
The player, who made 15 Serie A appearances at Milan, scoring twice, says he is "raring to go" with the Verona club next season.
"I am happy because I had a good first half of the season and the second wasn't so good. I thank the club for their faith in me and will give my all to repay them," Birsa told Chievo's official website.
"I like to help my team-mates to score goals and to get them myself, but I am working on helping out more in defence.
"I believe that if you help the team out, then your own qualities emerge too. I spoke to the coach, he put a great deal of faith in me and his words were very important in getting me to sign the contract.
"I am here, raring to go and want to do well for the side. I have to be ready, as it gets serious now."
Eugenio Corini's side finished 16th in Serie A last term - two places and four points above the relegation zone.