Ogbonna has joined the Old Lady on a five-year contract after a 13m fee was agreed between the two Turin sides.
"I always look to the present and future," he said.
"I don't consider myself as a traitor because I have always underlined that we players are professionals. My heart belongs to football and football is played in all parts of the world.
"I think every player has ambitions of playing at the highest levels. My choice is not because I wanted to betray anybody, it was made because I'm ambitious.
"The derby? It will be important, but I have never pulled out of a challenge. Behind my passion is the desire to cause all opponents problems."