News of Elkins' move comes in the wake of other changes to Coke's marketing team across the globe, including the high profile departures of global chief marketing officer Marcos de Quinto in March and Ivan Pollard, senior vice-president of Coca-Cola North America, two months later.
Elkins has joined McKinsey as a partner. His role is focused on growing the business through marketing and sales.
He held his most recent post at Coca-Cola for over four years. Before that Elkins spent two years as commercial director, digital and three years as strategy and insights director.
He joined Coca-Cola in June 2006. Before his career at the drinks firm, Elkins was a manager at Marakon Associates.
A spokeswoman for Coca-Cola confirmed Elkins' departure and added that he has been replaced by David Martin, who was previously Coca-Cola's digital director, Europe.
Other senior management changes at Coke have included the stepping down of chief executive Muhtar Kent in December last year.
This summer, Coke launched a pair of crowdsourcing challenges in an attempt to find new natural calorie-free sweeteners that could be used in its drinks. The company is offering a $1m (£774,000) prize for whomever comes up with the "next stevia". Stevia was used in its recently axed Coca-Cola Life variant, which combined the natural sweetener and sugar in its recipe.