The 18-year-old travelled to Milan on Monday to undergo a medical and to complete contract negotiations with the Serie A giants, with the club and Castaignos having been in talks for several weeks already.
Feyenoord and Inter had already reached an agreement about a transfer fee in the region of €4 million in the January transfer window.
Castaignos is a product of the Feyenoord youth academy and has developed into an important first team player this season. The Holland under-19 star has so far scored nine goals in 28 Eredivisie appearances for the Stadionclub.
Inter were initially considering farming Castaignos out on loan to Feyenoord for the 2011-12 season, but the Nerazzurri are now planning to integrate the young forward into their first team from his arrival.
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