The rearrangement of Cu surfaces under electrochemical conditions is known to play a key role in the surface activation for major electrocatalytic reactions. Despite the extensive experimental insights into such rearrangements, from surface-sensitive spectroscopy and microscopy, the spatial and temporal resolution of these methods is insufficient to provide an atomistic picture of the electrochemical interface. Theoretical characterization has also been challenged by the diversity of restructuring configurations, surface stoichiometry, adsorbate configurations, and the effect of the electrode potential. Here, atomistic insight into the restructuring of the electrochemical interface is gained from first principles. Cu(100) restructuring under varying applied potentials and adsorbate coverages is studied by grand canonical density functional theory and global optimization techniques, as well as ab initio molecular dynamics and mechanistic calculations. We show that electroreduction conditions cause the formation of a shifted-row reconstruction on Cu(100), induced by hydrogen adsorption. The reconstruction is initiated at 1/6 ML H coverage, when the Cu-H bonding sufficiently weakens the Cu-Cu bonds between the top- and sublayer, and further stabilized at 1/3 ML when H adsorbates fill all the created 3-fold hollow sites. The simulated scanning tunneling microscopy (STM) images of the calculated reconstructed interfaces agree with experimental in situ STM. However, compared to the thermodynamic prediction, the onsets of reconstruction events in the experiment occur at more negative applied voltages. This is attributed to kinetic effects in restructuring, which we describe via different statistical models, to produce the potential- and pH-dependent surface stability diagram. This manuscript provides rich atomistic insight into surface restructuring in electroreduction conditions, which is required for the understanding and design of Cu-based materials for electrocatalytic processes. It also offers the methodology to study the problem of in situ electrode reconstruction.