I don't know when it started, but a lot of people think of him that way. Most people think of God as an elderly man because you have more wisdom as you age. Also, God is older than all that is, because he is the creator, so being old makes sense. Besides, since no one really knows how God looks, we want to have something to relate him to so we can have a picture in our mind.
I believe it was just artists trying to capture what an all knowing, ageless creator would look like to them. No one has actually seen God but we do see His creation all around us. Maybe the artist looked like how he depicted God as we are all made in His image.