The one catch here is that you can't simply upload an animated GIF to Facebook and expect it to work as intended. Instead, the image has to be hosted elsewhere; if it already lives somewhere on the web, you can just grab that link, or you can upload your own image to a site like Imgur. Pasting a link to a GIF in your status box will do all the necessary embedding for you, just as it does with links and YouTube videos.
On another interesting note, the animations don't automatically play, but instead require a click before they begin moving. That's a funny decision on Facebook's part, considering it has no qualms with letting its advertisers' videos and other embedded clips automatically play as a user scrolls past them.
Update 11:40am, May 29: Unfortunately, as the Daily Dot discovered this morning, the new GIF support does not yet extend to pages.
Illustration by Max Fleishman