There is a good feeling you get when your curiosity is satisfied, especially if is about a question you found interesting or important, or have spent a lot of time and energy trying to answer. Depending on how much I wanted to know, this feeling can be quite pleasing. Is there a word specifically for either the satisfaction of a curiosity, or the feeling that results?
I feel sated when a need has been fulfilled, including curiosity, for example: "Learning of the contents of the box in the movie "7" has sated my, and Brad Pitt's, curiosity."
Sate - verb, Sated - adjective
"having one's appetite completely satisfied"
This is what you get from Google Books Search, with the search term,
curiosity was [v*].
The best options seem to be:
All these words are quite generic, though. I did not see anything relevant that goes better with "curiosity" than with anything else.
I would like to call "satisfaction of curiosity" as knowledge (or knowing) if we really want to go with a single word. Because you know something when you satisfy your curiosity.
curiosity: A desire to know or learn.
Though, there isn't a single word for satisfaction that is only associated with curiosity. In most cases, "satisfaction" or "satisfied" can be used depending on the context.
The common phrase is "satisfy one's curiosity" as you mentioned in the question.
Other than that, relief and reward is used in some technical sources.
The drive to learn new information or perform some action is often initiated by the anticipation of reward (an emotional sensation of relief and happiness). In this way, the concepts of motivation and reward are intrinsically tied to the phenomenon of curiosity.
Perhaps enlightened, apprised, or informed?
enlightened - "Made aware of something."
apprise - "To notify, or to make aware; to inform."
informed - "Instructed; having knowledge of a fact or area of education."
Of the three, I'd go with enlightened as it seems to have the most positive connotations (to me at least).
I would say that my curiosity is satiated (rassasier in French).