The 19-year-old striker was one of the first summer signings from Feyenoord.
"It's true I have a good rapport with the goal and playing for a top club it might be even easier," he told Inter Channel.
"It's difficult to explain how happy I am at joining a great side like Inter. I know all the Nerazzurri champions, above all Wesley Sneijder because he's Dutch."
Castaignos is nicknamed the 'new Thierry Henry' for his pace and scoring record, having netted 15 goals in 27 games for Feyenoord last season.
"Many people have said I am similar to Henry, but I am me and he is him."