Gabbiadini has scored eight goals in all competitions for Samp and moves to Naples in a reported 13million euro deal.
The 23-year-old, who has two caps for Italy, was part-owned by Sampdoria and Juventus, with the two clubs splitting the fee equally.
Strinic is an experienced Croatia international and has previously played for Hajduk Split.
Napoli said in a statement on their official website: “Napoli have signed Ivan Strinic on a permanent deal and secured the outright purchase of Manolo Gabbiadini.
“The Croatian defender will take the number three shirt and the new Azzurri striker will wear number 23.”