White will take on the role leading the broadcasting and telecoms regulator in late March 2015.
In her 25-year public sector career, White has worked at the No 10 Policy Unit, the World Bank, the Department for International Development, the Department of Work and Pensions, the Ministry of Justice and the Treasury.
Dame Patricia Hodgson, the Ofcom chairman, said: "Sharon brings with her an outstanding combination of intellect, political acumen and experience leading complex public organisations.
"The Ofcom board is confident that Sharon will provide the leadership and vision to ensure Ofcom continues to promote a thriving communications sector in the UK that operates in the public interest."
Richards steps down this month after eight years in charge at Ofcom. Until White’s arrival Steve Unger, the director of Ofcom's Strategy, International, Technology and Economist Group, will step up to acting chief executive.