San Francisco - Apple on Monday announced that Tim Cook will step down as the tech giant's chief executive officer in September, handing the top job to company veteran John Ternus.The announcement answers long-simmering questions about a successor for 65-year-old Cook, who said he will become executive chairman of the board when he cedes Apple's CEO position.'It has been the greatest privilege of my life to be the CEO of Apple and to have been trusted to lead such an extraordinary company,' Cook said in a statement.