There are two unrelated tricks that are each commonly referred to as “Two-Card Monte”.
The most common use of the term refers to Theodore DeLand's marketed “Two Card Monte”, 1913 (see The Sphinx, Vol. 12 No. 6, Aug. 15 1913, p. 119).
The original trick did not include the move that now bears its name. In fact, the original was more of a gag. The performer would show both cards, place one on the table face up, and the other face down. After covering the face-up card with his hand, the performer would bet that the spectator couldn't guess what the face-down card was. The card was then turned over to reveal that it was a double-backed card.
The routine and handling now commonly referred to as “Two-Card Monte” is actually Frank Lane's marketed "The New Two Card Monte", 1931 (misspelled “Frank Land” in the instruction sheet, but see for example the ad in The Linking Ring, Vol. 11 No. 5, July 1931, p. 605). It used the sliding display move now connected with the trick, along with the behind-the-back guessing aspect.
The finessed optical deception, called the Optical Monte Move as well as the Two-Card Monte Move, in which the cards are fanned or crossed and the corners lightly flicked as they are displayed and switched, was invented by Neal Elias. It appeared in his At the Table, 1946, p. 10.
Around the turn of the twenty-first century, magicians also began using the “Two-Card Monte” title for a double card transformation performed by David Blaine on his television special, Street Magic, May 1997. Apart from the name, this trick shares nothing in common with DeLand's.
The trick Blaine performed has its roots in Eddie Fechter's “Be Honest What Is It?” from Magician Nitely, 1974, p. 10. However, there are many differences between these two tricks. The missing links for the evolution of Fechter's trick into what Blaine performed are Tom Ogden's “The Subtle Switch” from M-U-M, Vol. 71 No. 11, Apr. 1982, p. 16; and Paul Gertner's identically titled, but heavily varied, “Be Honest What Is It?” from the videotape Secret Sessions #3, c. 1995. Even though Gertner's handling makes several advances, he erroneously claims that it's Fechter's, straight out of Magician Nitely. The handling David Blaine used was essentially Paul Gertner's, but without the card-to-pocket finale.
An early precursor to this type of routine can be found in Ottokar Fischer's Illustrated Magic, 1933, p. 119. Fischer describes a trick in which the red Aces are placed on the table and seemingly mixed around. The audience is tasked with keeping track of which red Ace is where. When turned over, the two cards are found to be the black Aces.