Moveable is the older spelling of the adjective meaning capable of being moved. But movable is now the preferred form in all main varieties of English, and this has been so for over a century. The preference extends to derivatives such as immovable and movability.
Both words are accepted, however. On the web, movable appears about three times as often as moveable, and this ratio is roughly borne out in recent books and in current news stories from throughout the English speaking world. British writers tend to use moveable a little more often than the rest of us, but they still prefer movable by a significant margin.
This ngram graphs the use of movable and moveable in a large number English-language books published in the last two centuries. It shows the switch from moveable to movable occurred long ago, though, somewhat interestingly, moveable has stayed steady while movable has declined.
Both spellings are easily found in sources from throughout the last few centuries:
This system of pullies, some moveable and some fixed, and all embraced by the same cord, is called by some a tackle. [The economy of nature, by George Gregory, 1799]
Movable pulleys are generally used in combination with fixed pulleys. [Introductory course of natural philosophy, by Adolphe Ganot, 1881]
All the gear was lashed to the deck, but, nevertheless, everything moveable was swept by the seas, much of it being lost overboard. [Bay of Plenty Times (1911)]
The East German Communists today tightened their grip on East-West Berlin border traffic by ordering the installation of movable barriers … [via Milwaukee Journal (1961)]
Descending from the rafters on flying saucers or putting the drummer on a moveable platform that turned him upside down was not enough. [New York Time (2000)]
For this store is lined with wooden shelves, along which trundles a movable ladder, and is sprinkled with beaten-up metal worktables. [Telegraph (2012)]