Provided are a thermally conductive silicone composition excelling in heat resistance and thermal conductivity, in which thickening in an uncured state is suppressed, and which has excellent handling ease; and an electrical/electronic apparatus in which the thermally conductive silicone composition is used as a member.The thermally conductive silicone composition comprises (A) 100 parts by mass of either i) (a1) an organopolysiloxane having, in each molecule thereof, at least one alkoxysilyl-containing group bonded to a silicon atom and expressed by the general formula: and as generally described herein, or ii) a mixture of component (a1) and (a2) an organopolysiloxane having in each molecule thereof, at least two alkenyl groups but not the alkoxysilyl-containing group. In the mixture, the content of component (a1) is 10 to less than 100 mass %. The thermally conductive silicone composition further comprises (B) 400 to 3,500 parts by mass of a thermally conductive filler.