Ovid
Heroides, letter 2 (Latin: "exitus acta probat"), late 1st century BC
In Ovid's poem it is spoken by a heroine in a letter, so it is far from being a political philosophy.
the myth (Niccolò Machiavelli): Machiavelli is the usual suspect, but the sentence is not in The Prince. The Latin line in Ovid, "the outcome proves the deeds", is the oldest known source.
Source: Wikiquote