It is frequently rendered in the shorter form The proof is in the pudding, which dates back to the 1920s and came into common use in the United States in the 1950s. The American Heritage Dictionary trims it even further, to proof in pudding.
The current phrasing is generally credited to Miguel de Cervantes in Don Quixote (1615), via the popular 1701 translation by Peter Anthony Motteux. Motteux' translation of the book is famously loose. Cervantes' original phrase is al freír de los huevos lo verá, "you will see it when you go to fry the eggs. Motteux also snuck the "eggs in one basket" proverb into the Quixote.
Rogers' Dictionary of Cliche and the Oxford Dictionary of Quotations date it to the 14th century as "Jt is ywrite that euery thing Hymself sheweth in the tastyng", and William Camden stated it in 1605 in Remaines of a Greater Worke, Concerning Britaine as "All the proofe of a pudding, is in the eating".