"The president died at a hospital here in Singapore at 6.47 pm local time," Bangladesh High Commissioner in Singapore M. Mahbubuzzaman told AFP by phone.
Rahman, who was suffering from kidney and respiratory problems, was flown to Singapore's Mount Elizabeth Hospital by air ambulance on March 10 after his condition worsened.
His secretary Shafiul Alam told AFP that Rahman, a close aide of the nation's founding leader Sheikh Mujibur Rahman, had been suffering from "old age complications".
The former deputy chief of the ruling Awami League party, the country's 19th president, leaves a son who is a lawmaker and two daughters.
Prime Minister Sheikh Hasina and the parliament speaker, who has been discharging the day-to-day job of the president in Rahman's absence, sent their condolences.
Rahman's wife Ivy Rahman, also a politician, died in August 2004 after she was critically injured in a grenade attack on an Awami League party rally that also killed 20 other people.