The 25-year-old, who scored 10 goals and made 10 assists in the Serie A last season, underwent medical tests on Monday before signing the contract with the Naples club which finished second to Juventus in the 2017-18 league.
Verdi had been on the verge of a move in January and the two clubs agreed terms, but he turned it down, insisting he wanted to end the season with Bologna, who purchased the player for 1.5 million euros in the 2016 summer.
He has scored 16 goals in 62 appearances over the last two terms for Bologna.
Born in Broni, Pavia, Verdi came through the youth ranks at AC Milan but only made two senior appearances for them - in the 2009/10 Coppa Italia -- before moving to Torino.
Simone played 12 games for Torino in Serie B in 2011/12 and four in Serie A the following season before switching to Juve Stabia in January 2013, where he racked up a further 20 matches in Serie B.
That summer he joined Empoli, also in Serie B, and helped them gain promotion to the top flight weighing in with five goals in 40 matches.
In 2014/15 Verdi featured 26 times and scored once in Serie A.
After a brief spell in Spain with Eibar (making nine appearances in the Primera Division), he returned to Italy and spent the second half of the 2015/16 campaign with Carpi, notching three goals in eight games.
That was enough to prompt Bologna to sign him in the summer of 2016.
At international level, he has five U21 caps (one goal) and four caps for the senior side.
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