While false shuffles and mixing procedures date back to the earliest conjuring texts, false riffle shuffles didn't begin appearing in print until the mid-19th century. Jean Eugène Robert-Houdin described a push-through shuffle in Les tricheries des Grecs devoilées, 1961, p. 168 of the English translation. This style of shuffle was later described more fully in John Nevil Maskelyne's Sharps and Flats, 1894, p. 138.
In S.W. Erdnase's Expert at the Card Table, 1902, p. 161-164, the author describes a few unweave techniques to return the two halves of the deck back their original order. This technique is the basis of the Zarrow shuffle, which was published in The New Phoenix, No. 346, July 20 1957, p. 210.
David Ben provides a thorough survey of the development of false shuffles – and particularly the Zarrow shuffle – in Genii, Vol. 71 No. 2, Feb. 2008, p. 61.