Behera was born in a Brahmin family in the village of Kashibahal, a former state of Kalahandi. He was educated at Bhawanipatna and graduated in 1935. In 1939 he obtained a degree in physics from Ravenshaw College in Cuttack then went on to graduate with a degree in civil engineering from the Bihar College of Engineering in Patna in 1943. He served an apprenticeship with the Department of Works and Irrigation in the former state of Mysore, Government of Orissa, and in February 1945 was appointed as an assistant engineer in the Jog Hydro power project, where his special assignment concerned irrigation under the Kalindi, Darbar.Bhubaneswar Behera was married to Uma Devi. He has a daughter, Professor Yashodhara Mishra, and three sons: one is a medical doctor, another a police officer Binay Behera, and the third a railway officer.
Behera came across the perennial Indravati flowing across the Thuamul Rampur Plateau of Kalahandi, a tributary of the Godavari, running parallel to the Eastern Ghats. He visualized the diversion of the river Indravati to the Hati River to create an artificial waterfall from a height of 2,000 feet. This artificial waterfall would generate hydroelectric power that would ensure the perennial supply of water for irrigation. He prepared a preliminary scheme for the same and submitted it to the Maharaja for consideration. The Maharaja was thrilled with his work