Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) remained genetically stable during the first 3 months of the pandemic, before acquiring a D614G spike mutation that rapidly spread worldwide and then generating successive waves of viral variants with increasingly high transmissibility. We set out to evaluate possible epistatic interactions between the early-occurring D614G mutation and the more recently emerged cleavage site mutations present in spike of the Alpha, Delta, and Omicron variants of concern. The P681H/R mutations at the S1/S2 cleavage site increased spike processing and fusogenicity but limited its incorporation into pseudoviruses. In addition, the higher cleavage rate led to higher shedding of the spike S1 subunit, resulting in a lower infectivity of the P681H/R-carrying pseudoviruses compared to those expressing the Wuhan wild-type spike. The D614G mutation increased spike expression at the cell surface and limited S1 shedding from pseudovirions. As a consequence, the D614G mutation preferentially increased the infectivity of P681H/R-carrying pseudoviruses. This enhancement was more marked in cells where the endosomal route predominated, suggesting that more stable spikes could better withstand the endosomal environment. Taken together, these findings suggest that the D614G mutation stabilized S1/S2 association and enabled the selection of mutations that increased S1/S2 cleavage, leading to the emergence of SARS-CoV-2 variants expressing highly fusogenic spikes. IMPORTANCE The first SARS-CoV-2 variant that spread worldwide in early 2020 carried a D614G mutation in the viral spike, making this protein more stable in its cleaved form at the surface of virions. The Alpha and Delta variants, which spread in late 2020 and early 2021, respectively, proved increasingly transmissible and pathogenic compared to the original strain. Interestingly, Alpha and Delta both carried the mutations P681H/R in a cleavage site that made the spike more cleaved and more efficient at mediating viral fusion. We show here that variants with increased spike cleavage due to P681H/R were even more dependent on the stabilizing effect of the D614G mutation, which limited the shedding of cleaved S1 subunits from viral particles. These findings suggest that the worldwide spread of the D614G mutation was a prerequisite for the emergence of more pathogenic SARS-CoV-2 variants with highly fusogenic spikes.