The 55-year-old, who was the bishop of the town of Crediton in Devon, takes over her London role from Dr Richard Chartres, who retired in February, Downing Street said today.
Legislation to allow women bishops was formally adopted by the Church of the England in 2014.
Mullally, the daughter of a hairdresser and among the most prolific bishops on Twitter, vowed to be "a bishop of London but also for London".
"It is a great honour to be nominated to the See of London. Having lived and worked in London for over 32 years, the thought of returning here is about returning home," said Mullally.
Before becoming a priest, the bishop worked as a nurse in the state-run National Health Service (NHS) hospitals in London, including St. Thomas's and the Royal Marsden, and became chief nursing officer in 1999.
She was ordained as a priest in 2001.
In 2005, she was made a Dame in recognition of her services to nursing.
She said in her statement: "I am often asked what it has been like to have had two careers, first in the NHS and now in the church. I prefer to think that I have always had one vocation: to follow Jesus Christ, to know him and to make him known, always seeking to live with compassion in the service of others, whether as a nurse, a priest, or a bishop.
"To be given the opportunity to do that now in this vibrant world city is a wonderful privilege."
Her diocese covers much of Greater London north of the Thames, from Staines to the Isle of Dogs and north to Enfield.
It includes more than 70,000 regular worshippers, 1,000 clergy and ministers, 150 church schools and the 1.5 million people who visit or worship in St. Paul's Cathedral every year.
Bishop Sarah, who is married with two adult children, will be formally installed as the 133rd Bishop of London by the Archbishop of Canterbury, Justin Welby, at the Cathedral early next year.
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