The merger will see Age Exchange, which runs an arts centre for older people in Blackheath, retain its own trustees, registration, buildings, branding and executive team but become a subsidiary of CIC.
The merger was finalised on 27 July but was announced on Friday.
CIC employs more than 5,500 staff throughout England and Scotland. Age Exchange employs 16 people. No job losses will occur as part of the merger, the charities said.
Age Exchange said that the merger would allow it increase its reach and grow as an organisation, while CIC could improve its dementia services as a result of the partnership.
According to the Charity Commission's website, Age Exchange had an income of £732,792 in the year to 31 March 2017 and CIC had an income of £114.9m during the same period.
Age Exchange had sought a national social care charity as a partner to help it expand its services and selected CIC because of its national infrastructure and commitment to dementia services.
Rebecca Packwood, chief executive of Age Exchange, said: "We set out to find a national partner that provided both the infrastructure we needed to grow and synergy in terms of values and ambition – CIC was the perfect candidate.
"This partnership will allow us to replicate the work we do in our Blackheath centre across the UK, dramatically increasing the number of beneficiaries we are able to reach."
Mark Adams, chief executive of CIC, said: "This represents a fantastic start to our bold new five-year strategy as we begin to go back to our charitable roots, putting the people we support, our colleagues and the community at the heart of what we do."