I’m sure this has been asked, but the nature of the request makes it difficult–nigh impossible–to search for the previous relevant posts. (Both words are rejected by the search engine as too common or too short.)
My WAG is that it originates as a question about what’s “up on the board” or something like that, i.e., what’s on the list of things to get done today.
The earliest work I remember seeing the phrase in is Mark Twain’s 1884 The Adventures of Huckleberry Finn (chapter 13):
(emphasis mine)
I can’t say anything about its origin, but it goes back at least farther than 1884.
In context here, it may suggest a meaning more along the lines of “What’s the matter?” as opposed to the modern “What’s happing?/What’s going on?” But that isn’t conclusive; it would still fit in context with the modern meaning.
That source above does not address the origin of the phrase at all, simply the Bugs Bunny version, What’s up, doc. (And ‘outlived Bugs Bunny’? He’s dead?)
Here’s the real nitty-gritty from OED.
up, adv. 2
From this there is a natural development to mean ‘what’s happening, what’s going on’.
I remember as a kid I asked my grandparents (one from Puerto Rico and one from Mexico) how to say “What’s up” in Spanish. They looked puzzled. Apparently there’s no direct translation. “Que arriba?” just makes people look up. Translating the meaning is “que pasa?” which really means “what’s happening?” but is the Spanish equivalent of “what’s up?”