The agency picked up the business following a competitive pitch handled by the AAR. The review of the account began in May.
Traditionally the charity has used a number of agencies in the past, such as Red Bee Media, on a project-by-project basis. However, the charity is now looking to raise awareness of its extensive work in the UK.
The work will cover a broad range of activity from local first aid provision and learning, to loaning medical equipment such as wheelchairs, to high-profile fundraising events.
The charity is also keen to engage and build relationships with younger audiences as it looks to expand the scope of its reach in terms of volunteers, donors and those who use its services.
Fiona Smith, head of marketing and brand development at the British Red Cross, said: "The Red Cross is known throughout the world for its work responding to international disasters, but we also do a vast amount of work here in the UK."
Nigel Roberts, creative director at Leagas Delaney, said: "The British Red Cross is an incredible, iconic organization.
"But most people only know it for its role in large scale disaster relief. We want to make sure that everyone is also fully aware of the lesser-known, vital services it delivers throughout the UK."