While SARS-CoV-2 likely has animal origins, the viral genetic changes necessary to adapt this animal-derived ancestral virus to humans are largely unknown, mainly due to low levels of sequence polymorphism and the notorious difficulties in experimental manipulations of coronavirus genomes. We scanned more than 182,000 SARS-CoV-2 genomes for selective sweep signatures and found that a distinct footprint of positive selection is located around a non-synonymous change (A1114G; T372A) within the Receptor-Binding Domain of the Spike protein, which likely played a critical role in overcoming species barriers and accomplishing interspecies transmission from animals to humans. Structural analysis indicated that the substitution of threonine with alanine in SARS-CoV-2 concomitantly removes a predicted glycosylation site at N370, resulting in more favorable binding predictions to human ACE2, the cellular receptor. Using a novel bacteria-free cloning system for manipulating RNA virus genomes, we experimentally validated that this SARS-CoV-2-unique substitution significantly increases replication in human cells relative to its putative ancestral variant. Notably, this mutation's impact on virus replication in human cells was much more significant than that of the Spike D614G mutant, which has been widely reported to have been selected for during human-to-human transmission.