BSC has initially bought 4.5 million ordinary shares at £1 a share, giving it a 38.7 per cent holding in the institution.
It plans to invest in two further tranches totalling £10m in 2015 and 2016, which is expected to take its holding up to about two-thirds.
Patrick Crawford, chief executive of Charity Bank, said he anticipated that BSC would end up with an equity stake of about 67 per cent.
He said the investment would enable the bank to increase the amount it lends to charities from £55m currently to about £250m by December 2018.
The Charities Aid Foundation, which devised the initial concept for Charity Bank in 1992, took a stake in the bank in 2002 and in March converted its preference shares to ordinary shares worth 34.4 per cent of the business.
The bank said that 17 trusts and foundations accounted for the remaining 26.9 per cent stake.
Nick O’Donohoe, chief executive of BSC, said: "This investment by Big Society Capital reflects our support for Charity Bank’s plans to increase its lending by continuing to meet the needs of its customers, particularly small and medium-sized charities in the UK."
Crawford said the bank had started to talk to other potential investors after securing the BSC investment.
He said the bank hoped to be making a profit from 2016 and aimed to start paying a dividend to shareholders, which it had not yet done, before the end of the decade.
The bank relinquished charitable status last year so that it could continue operating as a bank under revised banking regulations.
Dominic Casserley, chair of CAF, said: "We are delighted that Big Society Capital is making a substantial investment in Charity Bank that will allow the organisation to greatly increase its support for charities and social enterprises.
"Everyone at CAF and CAF Bank remains committed to our mission to support the charitable sector and help create innovative new ways of underpinning the work of charities and other social purpose organisations. We wish Charity Bank continuing success in the future and, as a continuing investor, look forward to supporting the bank’s growth and impact."