Condolences from a student to a professor
I'm not sure that you 'violated the professor's privacy'. Googling his name seems altogether appropriate.

Still, I wouldn't say anything. Since he hasn't told you (and no one else has told you), it seems he doesn't want to discuss it with you. I would respect this. Thinking back to when I taught classes, I certainly would have appreciated the effort, but it also would make me just a tiny amount uncomfortable, particularly since I hadn't announced the death. 

By the way, I'm assuming you're an undergraduate and you only know him as a teacher. If you are a grad student and he is a prof in your subfield, I still would err on the side of not saying anything, but it could go either way depending on the personalities involved.