Burney was an alumnus of the Bareilly College in Uttar Pradesh.[2] He was an officer of the Indian Administrative Service of the Orissa cadre where he went on to become the chief secretary of the state.[3] He served as Home Secretary to the Government of India from February 1980 to August 1981. Between 1981 and 1984, he served as the governor of Nagaland, Tripura and Manipur and from 1987 to 1988, as the Governor of Himachal Pradesh and Haryana.[4][5] He was also a member and later chairman of the Fourth and Fifth Minority Commissions from 1988 to 1992[6] and was the chancellor of the Jamia Millia Islamia University in Delhi from 1990 to 1995.[7]
Burney authored the work Iqbal: Poet – Patriot of India.[8][9]