Bacardi announced the news yesterday, and the world's largest privately owned spirits firm said it will announce an interim successor shortly.
"Pending that announcement, the executive leadership team wil report to Facundo L. Bacardi, the company's chairman, and a fifth generation member of the Bacardi family," the company said in a statement.
Facundo Bacardi said: "Ed leaves Bacardi a stronger organization from his dedication to the company and its brands.
"We thank Ed for his commitment and passion to Bacardi and we all wish him well," he added.
During his time at Bacardi, the firm said Shirley helped reignite the company's global marketing with new campaigns for Bacardi rum, Dewar's Scoth and Martini vermouth, as well as Italian sparkling wines.
"Also during his time with Bacardi, the company acquired one of the hottest new brands in the industry with the addition of St-Germain elderflower liquer to the Bacardi portfolio of premium spirits," Bacardi said in its statement.