"He breathed his last at the Mount Elisabeth Hospital," a Presidential spokesman told PTI.
Bangladesh ambassador to Singapore said doctors proclaimed him dead at 6.47 pm (local time) when his only son, daughters and close relatives were present.
Rahman was admitted to the facility on Mar 10 as he was flown to Singapore by an air ambulance for critical lung infection, a day after he was rushed to Combined Military Hospital (CMH) at Dhaka cantonment.
Rahman, a veteran politician, who celebrated his 85th birthday earlier this month was installed as the ceremonial head of the state in 2009 after Awami League was elected in the landmark Dec 2008 general elections.
A lawyer by profession, Rahman was a close aide of Bangladesh's founder and Prime Minister Sheikh Hasina's father Sheikh Mujibur Rahman and is regarded as a key figure in consolidating the ruling Awami League's unity at different times after 1975 coup when Sheikh Mujib was killed along with most of his family members.
Bangladesh has announced a three-day state mourning. "The acting president announced the three-day state mourning for the death of President Zillur Rahman," a presidential spokesman was quoted by BSS news agency as saying.
Parliamentary speaker Abdul Hamid was made the acting president on Mar 14 to discharge the functions of President in accordance with the Constitution.