The 20 year-old has signed to the end of the season with the view to a permanent deal.
"I'm very happy because at Milan I can realise my dream of playing for a prestigious team of champions here in Italy," Felipe told Sky Sport 24.
Felipe has been labelled the new Marcos Cafu by certain Italian media sources.
"I'm not Cafu, I'm Felipe and I will do my best to justify my place on the pitch," he said.
"I'm ready to play and we will see what my medical tests say. Then I will be at the Coach's disposal and it will depend on him."