Boris Grigorievich was born on April 26, 1944 in village Left Rossosh, Voronezh region, USSR (now Rossosh, Voronezh, Russian Federation). He was born in the family of a soldier. His father, Grigory Mikhailenko, during the great Patriotic war, served as a military pilot in the squadron of Pokryshkin. Mother, Tatyana Mitrofanovna, served in the same regiment.
In 1971 Boris Grigorievich graduated with honors from the geological and geophysical faculty of Novosibirsk state University and entered the postgraduate study of the Computing center of the Siberian branch of the USSR Academy of Sciences.
In period 1974-1999 Boris Grigorievich was a junior researcher, senior researcher, head of the laboratory, Deputy Director of the Computing center of the Siberian branch of the Academy of Sciences of the USSR (now Russian Academy of Sciences). The center was transformed into the Institute of computational mathematics and mathematical Geophysics in 1997. In 1999–2014 he was the Director of the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, while continuing to head the laboratory of numerical simulation of seismic fields.
Since May 22, 2003 he was a corresponding member of RAS (Department of mathematical Sciences). Since May 29, 2008 was the academician of the Russian Academy of Sciences (Department of mathematical Sciences). He headed the Department of mathematical methods of Geophysics of mechanics and mathematics faculty of Novosibirsk University. Since 2010, he was also a Professor at the Department of Informatics and systems design of Tomsk Polytechnic University. Boris Grigorievich was an author of over 170 works and discoveries.
