A few thoughts here, much that are comments on previous replies
1) Unless there is an issue raised by the professor, you have no issue except for neurosis that you are giving yourself
2) The professor handed out his old exams previously and therefore should have no expectation of the questions remain confidential for future use
3) This is not cheating as no intention of you do to so can be shown
4) This is not an unfair advantage as every student in the class had equal opportunity to find student from year before to get old exam
(btw this was common in my original UG days as well as postbacc just a decade or so ago. Indeed the prof made old exams available and most students never bothered).
5) Unless the professor made a statement in class or on syllabus that students should not share old exam or current students seek them out, there can be no violation of any "honor" code. For example, the MCAT specifically forbids even discussing specific questions with anyone and you sign to that affect.
6) If the professor asks how you did so well, then you must explain what happened. To do otherwise, would be to violate honor code at most schools