We present a global analysis of the spread of recently emerged SARS-CoV-2 variants and estimate changes in effective reproduction numbers at country-specific level using sequence data from GISAID. Nearly all investigated countries demonstrated rapid replacement of previously circulating lineages by the World Health Organization-designated variants of concern, with estimated transmissibility increases of 29% (95% CI: 24–33), 25% (95% CI: 20–30), 38% (95% CI: 29–48) and 97% (95% CI: 76–117), respectively, for B.1.1.7, B.1.351, P.1 and B.1.617.2