The 22-year-old failed to impose himself at Bolton after a serious knee injury but he has enjoyed regular first-team football in Serie A.
The Italian side's president, Urbano Cairo told Sisport, "We have used our buy-out clause to sign Blerim Dzemaili from Bolton."
"He showed great qualities as a person and as a footballer. He is a top player with a bright future.
"He is part of our plans for the future."