The former Manchester United left-back said: "It will be impossible to make people forget Robert Carlos and I have not come here for that, we are different. It was admirable what he did here and I come to give everything.
"At Manchester United I played almost always as a fullback, whereas with Argentina I play at centre-half. The truth is that I feel good in both positions.
"It's true Olympique Lyon tried very hard for me, but I had decided on Madrid because every player wants to come to this club. I have thought about it and I believe that I have made the correct decision."
On the prospects of making tomorrow night's derby against Atletico Madrid, Heinze added: "We will see, I could not say right now. I have had personal problems and I have trained, but not with Manchester United.
"In the next training session, we will see if I can play or not, the trainer will decide."