The operator has seen consistent declines in its retail revenue, reporting a 6% year-on-year fall for the 16-week period ending 14 October.
Rank Group brand Mecca saw its retail fall by 5% for the same period despite enjoying 6% growth on its digital channels.
Morgan joined Rank in 2016 to run Mecca’s retail business and led the overall UK retail division from 2017.
For the six months ending 31 December, meanwhile, Rank Group reported a 16% growth in digital revenue but saw a 2% fall in overall revenue, chiefly due to its retail and casino performance.
CEO John O’Reilly will assume Morgan’s day-to-day responsibilities until a successor is replaced.
Morgan said: "I have had a very exciting three years with Rank and feel now is the appropriate time for a new challenge."
O'Reilly said: "Alan has been instrumental in leading the transformation plan across the division and he leaves Rank with our best wishes for the future."
