How was Kingdom Hearts Conceived in the First Place?

The Kingdom Hearts video game series has an interesting premise: that of combining characters from the works of the Walt Disney company with characters from the works of Square Enix. To someone who is unfamiliar with the series, it may seem as if the idea occurred to someone when they were intoxicated; it is a completely random and ludicrous idea (not unlike that of the Mario series, as a side note: a turtle/dinosaur man has kidnapped the princess of the Mushroom Kingdom, and an Italian plumber must rescue her, gaining powerups from mushrooms and flowers? How bizarre is that?! Or what about Teenage Mutant Ninja Turtles? How random can a title be?) that utterly defies reason: how could two completely separate and dissimilar franchises be combined, and work so well?

I have never played any of the Kingdom Hearts games at the time of this post, but I know that they are very popular, so the idea of combining Disney character with Square Enix characters obviously must be working, but I still find myself wondering how the franchise started. Who conceived the idea, originally? Did some person just randomly decide one day to have a video game that combines the world of Disney with the world of Final Fantasy? Did someone say, "let us mix them together, and see what happens!"

What does anyone here know about the conception and origins of Kingdom Hearts?