Cooper, who served nine years as CEO and has been at Imperial for 20 years, will leave once her successor has been appointed, Imperial said in a statement that gave no reason for her departure.
"Alison has worked tirelessly and with great energy and passion... and the board would like to thank her for the tremendous contribution she has made," said Chairman Mark Williamson.
"During her tenure as chief executive, the business has been significantly simplified and reshaped to strengthen its long-term growth potential, and more than £10 billion ($12 billion, 11 billion euros) in dividends has been returned to shareholders."