James Henderson has been with the group for 29 years and is currently operations director with oversight for the UK retail business, online and William Hill's businesses in Australia and the United States.
He will take over as chief executive when Mr Topping, who has overseen a period of rapid growth for the company during his six years in charge, steps down at the end of this month.
William Hill, which is celebrating its 80th anniversary this year, is the UK's biggest bookmaker with 2,400 betting shops and an industry leading online operation.
Chairman Gareth Davis described Mr Henderson, who started with the company as a trainee manager, as a "natural bookie".
He added: "He understands gambling, he understands how technical it has become and he understands all the channels."
Mr Topping said: "I have enjoyed working with James for many years and am pleased to have appointed him to various important operational roles in that time.
"It is great to have seen him progress up through the business to the point of taking on the big job, the role of chief executive.
"As a 'one company man' I am naturally a big supporter of William Hill and its people, so I really wish James and the rest of our management team all the success in the world in continuing to take the company forward."