The global noncompact symmetry O(d, d) of string effective action is discussed in a general setting when d of the coordinates are compactified on torii and the backgrounds are independent of these compact coordinates. Wormhole solutions corresponding to spacetime geometries R1 × S1 × S2 and R1 × S2 and R1 × S2 and R1 × S3 are obtained from the reduced string effective action and the action is written in a manifestly O(d, d) invariant form. A general treatment is given for obtaining wormhole solutions of different topologies from dimensional reduction. For specific ansatz of internal metric and antisymmetric tensor field, the reduced action is shown to have a global SL(2, C) symmetry. The SL(2, C) and duality symmetries have been exploited to generate new configurations of internal fields which produce wormhole solutions in four spacetime dimensions.