Gabbiadini, 23, passed a medical at the weekend and put pen to paper on a contract with the Naples club on Monday.
Napoli president Aurelio De Laurentiis hinted last month that a deal was on the cards and the Italy international has now sealed his switch from the Serie A rivals.
Gabbiadini has scored seven goals in 13 Serie A matches this season, including four in his last four games in all competitions.
Strinic, 27, confirmed last month that he was set to move to Naples and the left-back's deal was also announced on Monday.
The Croatia international has spent four years with Ukrainian side Dnipro and could be in contention to face Cesena on Tuesday.
Gabbiadini, who was greeted by up to 1,000 fans at Naples airport on Sunday, could make his Napoli bow against champions Juventus on Saturday as he is suspended.
