During the evolution of SARS-CoV-2 in humans, a D614G substitution in the spike glycoprotein (S) has emerged; virus containing this substitution has become the predominant circulating variant in the COVID-19 pandemic. However, whether the increasing prevalence of this variant reflects a fitness advantage that improves replication and/or transmission in humans or is merely due to founder effects remains unknown. Here we use isogenic SARS-CoV-2 variants to demonstrate that the variant that contains S(D614G) has enhanced binding to the human cell-surface receptor angiotensin-converting enzyme 2 (ACE2), increased replication in primary human bronchial and nasal airway epithelial cultures as well as in a human ACE2 knock-in mouse model, and markedly increased replication and transmissibility in hamster and ferret models of SARS-CoV-2 infection. Our data show that the D614G substitution in S results in subtle increases in binding and replication in vitro, and provides a real competitive advantage in vivo—particularly during the transmission bottleneck. Our data therefore provide an explanation for the global predominance of the variant that contains S(D614G) among the SARS-CoV-2 viruses that are currently circulating.