Performing ab initio molecular dynamics simulations of open systems, where the chemical potential rather than the number of both nuclei and electrons is fixed, still is a challenge. Here, drawing on bicanonical sampling ideas introduced two decades ago by Swope and Andersen [ J. Chem. Phys. 1995 , 102 , 2851 - 2863 ] to calculate chemical potentials of liquids and solids, an ab initio simulation technique is devised, which introduces a fictitious dynamics of two superimposed but otherwise independent periodic systems including full electronic structure, such that either the chemical potential or the average fractional particle number of a specific chemical species can be kept constant. As proof of concept, we demonstrate that solvation free energies can be computed from these bicanonical ab initio simulations upon directly superimposing pure bulk water and the respective aqueous solution being the two limiting systems. The method is useful in many circumstances, for instance for studying heterogeneous catalytic processes taking place on surfaces where the chemical potential of reactants rather than their number is controlled and opens a pathway toward ab initio simulations at constant electrochemical potential.