Bowie moves to Verona for a Hibs record fee. They say it "substantially exceeds" the £4.4m Celtic paid for midfielder Scott Brown in 2007, though the terms haven't been disclosed.
"Firstly, I would like to thank Kieron for the way he has conducted himself over the last 18 months," Hibs manager David Gray said.
"He has been a pleasure to coach and he has been fantastic to work with both on and off the pitch.
"This is a life-changing move for him and his family. He has a bright career ahead of him and we wish him every success in Italy and in the future moving forward."
Hibs sporting director Malky Mackay added, "It has been a joy to watch him develop during his time at Hibs and see him progress through the international youth squads before making his first senior Scotland cap.
"There has always been speculation over Kieron, with several clubs submitting bids over the course of the transfer window. We have worked hard to secure a deal that reflects his true value and one that is in the best interests of Hibernian and all parties involved."