His parents were Andrei Michailovich Golitsyn (1729–1770) and his wife princess Elizabeta Borisovna Jusupova (1743–1770).
He was made a marshal to Grand Duke Konstantin Pavlovich of Russia on 28 November 1796 and on 18 March 1798 became a lieutenant general.
He transferred to a cavalry regiment on 27 November 1798 before finally retiring on 5 January 1800.
Boris joined the Napoleonic wars afterwards and took part in the 1813 siege of Danzig.
They had eight children: He died from a stroke, aged 55, and was buried at Saint Alexander Nevsky Monastery.