We show that electronic population can be switched adiabatically between the wells of a biased, asymmetric double quantum well (QW) structure. A time-dependent dc field guides an initial state along a smooth path to a state that is localized in a specified QW. General requirements for adiabaticity are determined that manifest the conditions in which the transfer process is optimal. The time duration of the perturbation is a sensitive parameter that influences strongly the outcome of the adiabatic passage. If the perturbation occurs too rapidly, the states mix, and a time-varying superposition state is created. However, if the requirements of adiabaticity are satisfied at all times during the perturbation, the system remains in a pure state, and evolves adiabatically to the final state. Various forms of the dc field are compared, and their relative performance evaluated. The optimal field for efficient adiabatic passage varies from structure to structure, and depends on the response of the system to the dc field. Complex field shapes can be used to produce multiple shifts in electronic density between the QWs. This procedure provides an effective means to perform adiabatic passage in semiconductor heterostructures, with smooth transitions, selectivity, and reversibility.