White is currently second permanent secretary at HM Treasury, where she is the lead official responsible for managing the UK's public finances, a role she has held for just over a year. She is due to join Ofcom in late March 2015 on a £275,000 salary, a significant increase on her £150,000 salary HM Treasury.
White will replace Ofcom's current boss Ed Richards, who is due to step down this month after eight years in post. Director Steve Unger will act as interim chief executive until she joins.
She has been at HM Treasury for three years and has been a civil servant since 1989. White has worked in numerous government departments, including the Department for Work and Pensions, the Ministry of Justice and the Department for International Development.
She started her career with spells in the British Embassy in Washington, the Number 10 Policy Unit and the World Bank. She has economics degrees from Cambridge and University College London.
Commenting on her appointment, White said: "The communications sector is vital to the economy and delivers essential services to everyone in the UK. I look forward to starting in this fascinating job and building on Ofcom's considerable track record."
HM Treasury declined to comment on the news.
However Ofcom chairman Dame Patricia Hodgson 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."
Ofcom is responsible for regulating the television, radio, telecoms and postal sectors. It is currently working on ensuring universal access to broadband, improving internet speeds and trying to eliminate the problem of 'not-spots' with poor mobile coverage.