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.

I'm assuming from my experience with Canadian academia that this is a test that is taken in class, you turn it in at the end of the period, and then your professor either gives them back, graded, or allows you to come to their office and see your graded test.

Before you meet with the professor, you should find out whether your friend should have had a copy of the exam. Yes, if you saw a copy of an exam that was not released after the exam, it could be considered a form of cheating and you might get in trouble.

If it was released to the class (or is a take home exam everyone had a chance to see), then there is no issue.

To be clear, I sincerely doubt you will get in trouble here. What you did is reasonable and expected, but at the very least, you should be prepared to explain the situation and know where the test came from. Maybe the professor would like to know who is leaking their tests.

I have had classes where professors kept their tests well-hidden enough that if someone had a copy, I would immediately have suspected them of wrongdoing. Without more details, it's impossible to know how your situation fits in.

While the other answers provide good advice how to handle the situation in a polite and diplomatic manner, we should nevertheless get the actual questions straight:

Is having access to past exams cheating and, if yes, could it be proven just by a good grade?

(1) No, having access to past exams does not constitute by any means a case of cheating.

(2) No, an (unusually) good grade cannot be taken as a proof of cheating.

The following describes the legal situation in Germany, where cheating in an exam actually has a pretty narrow definition: It is constituted by unauthorised behaviour during the exam, such as taking unapproved material into the exam, talking or communicating with another student, and so on – the exact cases of unauthorised behaviour are defined by your institution. However, you have to be caught in flagranti or by clear proof of an action you did during that exam.

The situation may be different in other legal systems.