Gallop, who left the equivalent position at the National Rugby League in June this year, will assume the role once Buckley completes work on a new broadcast deal in the next two months.
FFA chairman Frank Lowy said Buckley had offered to step aside for Gallop, but that Lowy wanted him to complete the broadcast deal before his departure.
"The broadcast deal is at the heart of the future of football in this country and it has been the most critical aspect of my work for the past 18 months," Buckley said.
"I told the chairman some time ago I was determined to negotiate the best possible deal to underpin the future growth of the game but that once done I would like to work with him and the board to identify a successor."
Buckley, often criticised during a turbulent time in charge of the code, played a key role in luring Gallop to the role and Lowy paid tribute to the legacy the former AFL administrator left the game.
"These discussions created the opportunity for us to consider Gallop as a successor to Ben," he said.
"Ben has worked tirelessly for football both at home and abroad and has steered the game through a difficult period of consolidation.
"He has the respect and thanks of the board for his contribution and he will remain a valued friend of the game.
"I wish him well for the future."
Gallop, currently overseas, will step in as chief executive before the end of the year and will bring with him a wealth of experience and contacts from his time in charge of the NRL.
"Mr Gallop comes to the job well-equipped to meet the challenges ahead," Lowy said.
"He is an experienced sports administrator of high standing and is widely respected across all sports."