It’s true that William Shakespeare used the phrase “what’s done is done” in his play, MacBeth (written some time between 1603 and 1607) in Act 3, Scene 2.
With them they think on! Things without all remedy should be without regard: what’s done, is done.
However, Shakespeare is not responsible for the phrase. The phrase uses done in the sense of “ended” or “settled” which is a usage dating back from the first half of the 1400s. It’s actually a derivative of the early 14th Century French proverb: “Mez quant ja est la chose fecte, ne peut pas bien estre desfecte.” Translation: ” But when a thing is already done, it cannot be undone.”
That being said, the spirit of the phrase is even older than the early 14th Century, dating back to the works of the Latin poet from the Republican period, Gaius Valerius Catullus (84 BC – ca. 54 BC). In his poem Carmen VIII, he wrote:
“Miser Catulle, desinas ineptire
Et quod vides perisse, perditum ducas.“
“Poor old Catullus, stop your whining
What you see is over, accept it’s really over.”