The SARS-CoV-2 pandemic has entered an alarming new phase with the emergence of the variants of concern (VOC), P.1, B.1.351, and B.1.1.7, in late 2020, and B.1.427, B.1.429, and B.1.617, in 2021. Substitutions in the spike glycoprotein (S), such as Asn501Tyr and Glu484Lys, are likely key in several VOC. However, Asn501Tyr had been circulating for months in earlier strains and Glu484Lys is not found in B.1.1.7, indicating that they do not fully explain those fast-spreading variants. Here we use a computational systems biology approach to process more than 900,000 SARS-CoV-2 genomes and map spatiotemporal relationships, revealing other critical attributes of these variants. Comparisons to earlier dominant mutations and protein structural analyses indicate that the increased transmission is promoted by the combination of functionally complementary mutations in S and in other regions of the SARS-CoV-2 proteome. We report that the VOC have in common mutations in non-S proteins involved in immune-antagonism and replication performance, such as the nonstructural proteins 6 and 13, suggesting a convergent evolution of the virus. Critically, we propose that recombination events among divergent coinfecting haplotypes greatly accelerates the emergence of VOC by bringing together cooperative mutations and explaining the remarkably high mutation load of B.1.1.7. Therefore, extensive community distribution of SARS-CoV-2 increases the probability of future recombination events, further accelerating the evolution of the virus. This study reinforces the need for a global response to stop COVID-19 and future pandemics.