The Italian outfit have trumped European champions Bayern Munich to sign the 18-year-old, who can play at left-back or in midfield.
Scotland Under-17 international Hickey had a year left on his Hearts contract and made 33 appearances for the club.
He becomes the first British player in Bologna's 111-year history. Hickey made his debut for Hearts last year aged 16, and two weeks later became the youngest player to start a Scottish Cup final in the modern era when he played against Celtic.
His only goal came in a 2-1 win against Edinburgh rivals Hibernian last year.
Former Hearts manager Craig Levein said in August that Celtic had made several offers for the player.
Bologna, who have not disclosed the length of Hickey's contract, intend for him to be part of their first-team squad. Sinisa Mihajlovic's side began the Serie A season this week with a 2-0 defeat away to Milan, and host Parma on Monday.
Bundesliga Bayern would have placed him in their second team, which plays in the German third tier.