We advance a holographic construction for the entanglement negativity of bipartite mixed state configurations of two disjoint intervals in (1+1) dimensional conformal field theories (CFT_{1+1}) through the AdS_3/CFT_2 correspondence. Our construction constitutes the large central charge analysis of the entanglement negativity for mixed states under consideration and involves a specific algebraic sum of bulk space like geodesics anchored on appropriate intervals in the dual CFT_{1+1}. The construction is utilized to compute the holographic entanglement negativity for such mixed states in CFT_{1+1}s dual to bulk pure AdS_3 geometries and BTZ black holes respectively. Our analysis exactly reproduces the universal features of corresponding replica technique results in the large central charge limit which serves as a consistency check.