Is having access to past exams cheating and, if yes, could it be proven just by a good grade?
You haven't said whether you were actually accused or not. I'm assuming that you are just worried about what might happen in the meeting that hasn't happened yet. 

The most honest way to proceed, though you may suffer for it, is to tell it exactly like it happened. You studied three weeks, you had access to old exam materials and used those to prepare. All you had in the exam was your memory and your skills. You had no knowledge of any question to be asked on this exam. 

If the professor thinks you cheated, then s/he is very naive about how the world works. Student fraternities typically keep records of old exams and students study from them. If the professor uses old questions they should expect that those questions are available. 

You might be asked for the source of the materials and you would be unwise to conceal them and might face larger issues if you try. 

As the answer of Azor Ahai suggests, make sure that what you did isn't explicitly forbidden by  available course materials. But I don't really see a way in which requirements could be stated that really disallow such a practice. It would be completely unenforceable. Doing well is not a crime. Studying hard is not a crime. 

If your professor disagrees and wants to punish you, I'd suggest taking it to a department head or dean, again explaining exactly what you did and how. 

If you suffer for honesty, then it is deeply unfair.