Zappia, who is currently vice-president of sports channels at Sky's Italian operation, joins on 1 February and takes charge of the sales, marketing and customer operations teams.
He replaces Brian Sullivan, who moved to become deputy chief executive of Sky Deutschland on 1 January and is to become its chief executive on 1 April.
Sullivan had been with Sky since 1996 and was credited as the driving force behind the launch of its high definition, 3D and Sky+ digital video recorder technologies.
Zappia has had past experience in customer acquisition and retention, for which he was responsible along with brand marketing at Sky Italia between 2003 and 2007.
Jeremy Darroch, chief executive of Sky, said: "I am delighted to announce such a high calibre appointment. Andrea will bring a wealth of experience and add further strength to the leadership team at BSkyB."