Genoa rejected a 10m offer from the Nerazzurri this week, instead opting to extend his contract until 2014 and increase his salary to over 1m a season net.
"I thank Genoa for the faith they have shown in me," said the wide attacker. "This is what I wanted. I hoped to remain at this club.
"The outfit have made some important economical sacrifices for me, but I've not decided to just stay here for the money.
"I'll continue to give everything for these colours, for these fans, for this club."