The bank, which has offered services to figures such as Lord Byron and Jane Austen, will launch the app more than 340 years after its historic foundation in 1672.
The creation of a full digital service follows the bank’s launch last year of a tax-management app.
Profits at the bank dipped slightly to £29.7m in the year to the end of March 2015, but deposits increased 20 per cent as customers looking for safer investments trusted their money to the bank’s coffers.
Huge growth in digital banking is causing the whole industry to catch up fast. A joint report by the British Bankers’ Association and Ernst & Young published in June revealed that by 2020 mobile use by customers will outstrip internet, branch and telephone banking combined.