While more can always be written, versions of this question have come up a couple times recently, and I have answered versions of it here and here.

The TL;DR is: Shorter than you might think. As short as a day to as long as six weeks after the last polls closed, depending on where you lived and how interested you were in hearing the news. Elections decided by Congress in 1800 and 1824, of course, took longer, but once Congress decided, the vast majority of Americans would have heard between one day and six weeks after the Congressional decision was made. More information in those earlier answers.

EDIT: Phrasing.