Presidential secretary Mohammad Shafiul Alam said Rahman died at Mount Elizabeth Hospital, where he was transported March 10 after experiencing respiratory problems, BDNews24.com reported.
Speaker Abdul Hamid, who has been fulfilling the presidential duties since Rahman's hospitalization, expressed shock at the news, as did other Bangladeshi government leaders, BDNews24.com said.
A veteran politician and member of the Awami League, Rahman became Bangladesh's 19th president in February 2009 in an uncontested election.
A lawyer, Rahman holds a master's degree and law degree from Dhaka University.
Rahman was elected to Bangladesh's parliament multiple times. Before Bangladesh won its independence from Pakistan, he was a member of the then-Provincial Assembly of East Pakistan in 1970.
He was jailed for four years following the assassination of the country's founding leader and first president, Bangabandhu Sheikh Mujibur Rahman, in August 1975. In 1986, he was jailed again while a member of parliament during a movement for restoration of democracy, the news site said.
His wife, Ivy Rahman, then-women affairs secretary of Awami League, died in a grenade attack during an Awami League rally in Dhaka in August 2004.