ADDIS ABABA, Jan 31 (Reuters) - The African Union formally admitted Morocco as a member on Tuesday, more than three decades after Rabat withdrew from the predecessor organisation.

Morocco's King Mohammed, who had been campaigning since last year to join, waved to applauding heads of state and delegates at the end of an annual summit in the AU headquarters in Ethiopia's capital.

The North African kingdom quit the AU's predecessor, the Organisation of African Unity, three decades ago amid a dispute about the body's recognition of Western Sahara, most of which has been controlled by Morocco since 1976.

(Reporting by Ed Cropley; Writing by Edmund Blair; Editing by Andrew Heavens) ((edmund.blair@thomsonreuters.com; +254 20 4991232; Reuters Messaging: edmund.blair.thomsonreuters.com@thomsonreuters.net))