It is the first time the charity has worked with a retained lead strategic and creative agency. Creature will "help mobilise humanitarian support for those in crisis".
Joint, Mcgarrybowen and VCCP also pitched for the business. The review was run through Oystercatchers.
The charity called the pitch in September last year. It has previously worked with Leagas Delaney.
Zoe Abrams, executive director of communications and engagement at the British Red Cross, said: We are excited about collaborating with [Creature of London] to innovate and enhance the impact of our engagement.
"Working together, our ambition is to mobilise the power of humanity in order to meet our organisational vision of a world where everyone gets the help that they need in a crisis."