In the Legend of Korra game (where you explore Republic City), when you click on the White Lotus guards, it says specifically. "When Aang realized his health was failing, he commanded the White Lotus to find and protect the next Avatar." Not exact words, close enough, but the best guess is something health-related- either something not-peaceful, like a heart attack, or passing in his sleep.
watch the legend of korra.
it tells you.
aang's cause of death though is not so clear, but it seems that it was just natural because if it wasn't, then people would talk about it and refer to it a lot more than they actually do.
just a helpful hint.
@BAmeliaVee, aang stayed for a hundred years in an ice-burg, i agree but, his body didn't change aka, he didn't grow up aka, he is supposed to be 166 years old but his body age is 66 years old, no way he died of old age. he was (80% sure of that) hunted down since katara is alive.
there is only 15% chance that he just passed away and a 5% chance that he gave up life. he may also have passed away due to sickness