John Lewis Partnership names new chair
She will succeed current chairman Sir Charlie Mayfield, who is set to step down in early 2020.
Mayfield admitted that White, who has previously worked in a number of government positions including senior roles at the Treasury and Ministry of Justice, was an unexpected candidate for the role.
"I readily recognise that Sharon is not the conventional retail choice. But these are not conventional retail times, nor is the Partnership a conventional company," he said.
"Sharon is an inspirational leader with the personal and professional skills to ensure the Partnership continues to innovate and change while at the same time retaining and strengthening our distinctive character and democratic vitality."
White said: "I am a passionate believer in the Partnership: Partners working together for each other's wellbeing with the confidence to invest for the long-term and a focus on delivering for our customers in a rapidly changing retail environment.
"John Lewis & Partners and Waitrose & Partners are not merely British retail icons, but also a model of a better way to do business."
Speculation over who would take the reins pointed to internal candidates such as finance boss Patrick Lewis or experienced retailers such as former WH Smith chief Kate Swann.
White is expected to step down from her role as CEO of Ofcom around the end of this year. The regulator will now begin looking for her successor.
Lord Burns, chairman of Ofcom, said: "Under Sharon's leadership, Ofcom has helped to deliver ultrafast broadband, widespread 4G mobile and now 5G, and became the first independent regulator of the BBC.
"She leaves Ofcom as a regulator with a relentless focus on the consumer interest; making sure people and businesses can get the best out of their communications services."