The account move is a further setback for Coca-Cola's roster network McCann-Erickson, which last week lost the business in France to the Havas-owned BETC Euro RSCG.
The Interpublic agency's New York shop was also dropped from Coca-Cola's US creative roster in January. It was replaced by the WPP agency Berlin Cam-eron/Red Cell.
Berlin Cameron developed the existing work, which uses Hollywood stars including Courtney Cox-Arquette and Penelope Cruz.
Coca-Cola first approached Mother for creative solutions for the Classic Coke brand in January. The agency's new above-the-line campaign is expected to be unveiled at the start of next year.
Coca-Cola operates a complicated roster system. The main Coke brand is supported by a variety of agencies including Wieden & Kennedy Amsterdam, Berlin Cameron and now Mother.
A campaign by McCann-Erickson Madrid is due to be aired on UK television.
Mother already handles the advertising for the Coca-Cola-owned brands Lilt, Schweppes, Oasis and Dr Pepper, but the Mother partner Andy Medd admitted this was the "big one".
He said: "This appointment is extremely important for Mother and we recognise the enormous responsibility on us to deliver brilliant communication for the most famous brand in the world.
"Coca-Cola has an amazing advertising history and we are thrilled to be given the opportunity to work on the brand."
A Coca-Cola spokeswoman said McCann will retain a place on the company's UK roster.
Julia Goldin, the marketing director for Coca-Cola Great Britain, said: "We always want to find the best creative for our consumers - campaigns that resonate with them and that they enjoy - and especially on brand Coca-Cola we look to surprise and delight our consumers.
"Mother's work for our other brands has been memorably ground-breaking and we're ready for more."
Coca-Cola is also in the process of reviewing its media buying account in the US, which is currently held by Universal McCann.