Burney, suffering from old age related ailments, died last night, a member of his family said.
Burney was an officer of the Indian Administrative Services of the Orissa cadre where he went on to become the Chief Secretary of the state.
He served as the Governor of Himachal Pradesh, Haryana and some northeastern states.
He was also the Chancellor of the Jamia Millia Islamia University in Delhi from 1990 to 1995.
Burney was a member and later chairman of the Fourth and Fifth Minority Commissions from 1988 to 1992.