Newly promoted Chief Operating Officer Tom Singer said the risk of the transaction being stopped by the Competition Commission is minimal.
Hills would eventually sell 30 to 50 of the Stanley shops in towns where regulators deem that the deal may cause competition problems.
The acquisition would give Hills a presence in areas in which it is currently under-represented or unrepresented. Particularly crucial are 52 Stanley shops in Ireland and a further 11 in the Isle of Man and Channel Islands.
"It's a natural fit to our estate and it actually allows us to have a uniform coverage all over the country," said David Hood, Director of Public Relations for William Hill.
"This acquisition represents a rare opportunity for William Hill to substantially increase its distribution reach, whilst simultaneously realising benefits of scale," said David harding, William Hill CEO.
"Having completed our due diligence we are confident that we will achieve substantial synergies by applying William Hills systems and approach to the enlarged estate," he added.
Stanley Leisure welcomed the sale of its betting shops, describing the Â£504m price as "very attractive".
Stanley Chief Executive Bob Wiper said the deal would allow the company to concentrate on the casino business. Stanley Leisure, with 41 venues, is the largest casino operator in the UK.
Stanleybet internet business is not part of the William Hill transaction, and according to Wiper, it may now be sold separately.
"We will now conduct a fairly quick review of our e- businesses, but we don't see them staying in the group in the long term,'' Wiper said.
Shares in William Hill were trading 3% lower.
As a result of the acquisition, the company would no longer return the Â£450m of capital to shareholders like announced back in March.