The story
Falsely attributed to Machiavelli's The Prince, which does not use the phrase in the work. A possible source is Ovid's Heroides (ca. 10 BCE), which says exitus ācta probat (“the outcome justifies the deeds”). However, its use there is quite likely to have an opposite meaning of outcome proving means were unjustified, based on its context.
Etymology from Wiktionary, CC BY-SA 4.0.