Glancey, who took on the top job in 2012 after four years as chief operating officer, steps down with immediate effect.
To assist with a smooth handover, he will stay the company until the end of February.
Former Müller Dairy UK chief executive Stewart Gilliland has been appointed executive chairman on an interim basis.
A non-executive director at C&C since 2012, Gilliland was appointed chairman in July 2018 and is also chairman of the nomination committee.
Lager brand Tennent’s
In addition to cider brands Magners and Bulmers, C&C manufactures, markets and distributes Scottish lager brand Tennent’s, made at Wellpark Brewery in Glasgow. It also manufactures a range of premium craft ciders and beers, including Heverlee, Menabrea and Orchard Pig.
The Dublin-headquartered company used the announcement to state that trading across the group for the four months to 31 December 2019, including the key Christmas trading period, had been in line with the board’s expectations.
It added that it was on track to deliver double-digit earnings per share growth for the current financial year.
Gilliland said the board would like to thank Stephen for his “significant contribution” to C&C over many years.
He added: “The company is well-positioned to continue to implement its established strategy to deliver value for shareholders and Stephen will continue to be available to help facilitate a smooth handover.”
Meanwhile, the Scotch whisky industry could be threatened by further tariffs from the US after the UK’s split with the EU, a workers’ union has claimed.