"I have it!" or "I've got it!"
You've made a great discovery. The story is that Archimedes worked out how water displacement works while he was in the bath. This was the answer to a problem he was working on. He screamed out "eureka!" (literally, "good discovery!") and ran down the street, naked.
Eureka has its origin in Greek and is taken from the word heurēka. This expression is supposed to be exclaimed by Archimedes when he discovered the way to measure the volume of an uneven solid. This method of Archimedes was then used to find out the purity of Gold objects. The word heurēka is actually the first person singular and perfect tense of heuriskein. The heuriuskein means to find. Thus, the exclamation eureka means I have found (it).
Today, this exclamation is widely used often in a humorous way. Eureka is used to show how one is that he has discovered the answer to a problem or has found something. Thus, this expression indicates triumph of finding or discovering something. Some words which could be used for 'eureka' but not in the form of an interjection are: solve, unriddle, discover, fathom, hunt out, satisfy, set at rest and determine.