The independent emergence late in 2020 of the B.1.1.7, B.1.351, and P.1 lineages of SARS-CoV-2 prompted renewed concerns about the evolutionary capacity of this virus to overcome public health interventions and rising population immunity. Here, by examining patterns of synonymous and non-synonymous mutations that have accumulated in SARS-CoV-2 genomes since the pandemic began, we find that the emergence of these three "501Y lineages" coincided with a major global shift in the selective forces acting on various SARS-CoV-2 genes. Following their emergence, the adaptive evolution of 501Y lineage viruses has involved repeated selectively favored convergent mutations at 35 genome sites, mutations we refer to as the 501Y meta-signature. The ongoing convergence of viruses in many other lineages on this meta-signature suggests that it includes multiple mutation combinations capable of promoting the persistence of diverse SARS-CoV-2 lineages in the face of mounting host immune recognition.