Provided is: a multicomponent curable thermally conductive silicone gel composition which has a high thermal conductivity, has excellent gap-filling ability and repairability, and has superior storage stability; a thermally conductive member comprising the composition; and a heat dissipating structure using the same. The thermally conductive silicone gel composition comprises: (A) an alkenyl group-containing organopolysiloxane; (B) an organohydrogenpolysiloxane; (C) a catalyst for hydrosilylation reaction; (D) a thermally conductive filler; (E) a silane-coupling agent or a hydrolysis condensation product thereof; and (F) a specific organopolysiloxane having a hydrolyzable silyl group at one end thereof. The thermally conductive silicone gel composition includes (I) a liquid composition that includes components (A), (C), (D), (E), and (F), but does not include component (B) and (II) a liquid composition that includes components (B), (D), (E), and (F), but does not include component (C) which are individually stored.