Basically since the Chromecast was released.
The Chromecast came out on July 24, 2013, and several dozen articles note the feature before the end of July (26-28th). Just click the little down arrow on the Chromecast button (part of the Chromecast extension) then "Cast entire screen (experimental)."
July 26th, 2013: http://www.droid-life.com/2013/07/26/tip-chromecast-can-cast...
July 26th, 2013: http://www.androidauthority.com/chromecast-share-entire-desk...
July 27th, 2013: http://forum.xda-developers.com/showthread.php?t=2380302
July 26th, 2013: http://www.reddit.com/r/Android/comments/1j3sd1/chromecast_c...