The present invention relates to a thermally conductive polysiloxane composition that provides a cured product having excellent tackiness and flexibility in which the composition contains (A) a thermally conductive filler, (B) a siloxane compound having an alkoxysilyl group and a linear siloxane structure, (C) a polyorganosiloxane having at least two alkenyl groups bonded to silicon atoms per molecule, (D1) a linear polyorganohydrogensiloxane represented by the general formula (4), (D2) a polyorganohydrogensiloxane having per molecule at least three units represented by the general formula (5), and (E) a platinum catalyst.