The 22-year-old replaces Gonzalo Higuain, who joined Juventus last week, at the Italian Serie A club.
"It's an honour I will become a part of Napoli with its amazing fans full of passion, a great club with a glorious history. I want to make these fantastic Napoli fans happy," he said on the Facebook page of F-MG media.
Milik's move came after an impressive showing at the European Championship where Poland reached the knockout stage even though he only became a regular with Ajax in the second half of the season in which he scored 21 league goals.
Ajax, who signed Milik from Bayer Leverkusen in 2014, have gone back on a statement they released three weeks ago in which they said he would not be sold.
Ajax play on Wednesday in the preliminary round of the Champions League against PAOK Salonika in Greece after being held to a 1-1 draw at home in the first leg.
