Bull, who joined Ladbrokes in 2011, will leave the company at the end of February next year, after it reports its full year results. If the Coral merger is completed before then, he will leave soon after completion.
When the two rival betting firms announced their partnership in July it was agreed Coral's chief financial officer Paul Bowtell would oversee the finances of the combined company.
Bull is now pursuing "other potential opportunities", the company statement said.
Chairman Peter Erskine said: “Ian has worked tirelessly through what have been challenging times and has helped steer Ladbrokes to this exciting point in its journey.
“We are pursuing an aggressive plan to build a stronger Ladbrokes as well as working on the proposed merger with the Coral Group, which will deliver substantial cost savings.
“In accepting his request we are pleased that Ian has reiterated his commitment to delivering our strategy and in leading the current refinancing of the group in preparation for the proposed merger. I am delighted that we will continue to benefit from Ian's energy and experience during this important time.”
Ladbrokes' share price was up 3.19 per cent at pixel time.