The tobacco company issued a profit warning that it blamed on the US regulatory crackdown on vaping, which has affected Imperial’s e-cigarette brand, blu.
Imperial revised its expected growth down to 2% from 4% last week.
Cooper, an ICAEW member, oversaw a reduction in the number of cigarette brands at Imperial, and its change of name from Imperial Tobacco to Imperial Brands.
The company is also looking for a new chairman, after Mark Williamson stepped down in February.
Cooper was one of only five female CEOs at FTSE 100 firms, alongside Emma Walmsley at GlaxoSmithKline, Dame Carolyn McCall at ITV, Liv Garfield at Severn Trent and Alison Brittain at Whitbread.
Alison Rose will become CEO of the Royal Bank of Scotland next month, the first woman to lead one of the country’s major high street banks.