Where does the idea of a Hadouken and Kamehameha come from? Having read a few manga/watched some anime, I have seen that many characters can use attacks where they gather their "ki" or, according to wikipedia, "Life force", and release it in a fireball like manner. The most widely known examples of these are the "Hadouken", and the "Kamehameha". Where does the idea for this kind of attack come from? Did one person think of it and everyone copy them, or is there like a old teaching or story about this?

Thanks in advance :)
I'm going to talk about the Kamehameha here if I talk about either one of them specifically, because I know more about Dragon Ball than I do about Street Fighter.

The Kamehameha is supposed to be the ultimate attack, in which the user gathers all of their Ki into one point and releases it at once.

Ki, also spelled Chi or Qi, is "life-force" as you mentioned. The idea of ki is one that is pervasive throughout East Asian mythology. It originates from tai-chi. Tai-chi is not just a martial art in the sense that someone brought up in the West like myself might think of it -- that is to say, it doesn't exist just so that you can learn to defend yourself from an assailant. It is a practice that was birthed from Taoism, also spelled as Daoism, which is a very spiritual set of beliefs.

Taoism, as you may know, has as one of its core principles the balance of internal and external force -- yin versus yang. Yin represents the internal force, and yang the external. 

In tai-chi, one does learn self-defensive techniques and weapon drills, it's true. However, one also learns to cultivate the yin in one's body. This may be an oversimplification but I believe that defensive and weapons training is considered the cultivation of yang. 

To cultivate yin, one learns completely passive techniques, such as breathing and meditation. These are designed to promote overall health and wellness of one's own body. To someone unfamiliar with tai-chi, the exercises might look like aerobics or even just stretching exercises. In mythology, it is believed that masters of such artistry can live for well over a hundred years, or even forever. (hint hint, Master Roshi, although it's explained in the show as him drinking from "The Fountain of Youth" -- that part is a parody of the "eternal martial artist" trope in Asian stories). The breathing and movement techniques are said to keep one's ki in balance, and cultivate untapped potential ki which has not begun to flow in the body yet.

In other words, although a show like Dragon Ball is fantasy, to explain it in real world mythology: Master Roshi became such a master of tai-chi that he can manipulate his ki into an external force directly.

The same principle applies to Ryu. He is supposed to be a master martial artist. To someone familiar with East Asian mythology and tropes, this means that he knows how to manipulate his life energy to make fireballs, to put it simply.