On 30th January 2020, an outbreak of atypical pneumonia caused by a novelbetacoronavirus, named severe acute respiratory syndrome coronavirus 2(SARS‐CoV‐2), was declared a public health emergency of international concern bythe World Health Organization. For this reason, a detailed evolutionary analysis ofSARS‐CoV‐2 strains currently circulating in different geographic regions of theworld was performed. A compositional analysis as well as a Bayesian coalescentanalysis of complete genome sequences of SARS‐CoV‐2 strains recently isolated inEurope, North America, South America, and Asia was performed. The results ofthese studies revealed a diversification of SARS‐CoV‐2 strains in three differentgenetic clades. Co‐circulation of different clades in different countries, as well asdifferent genetic lineages within different clades were observed. The time of themost recent common ancestor was established to be around 1st November 2019.A mean rate of evolution of 6.57 × 10−4substitutions per site per year was found.A significant migration rate per genetic lineage per year from Europe to SouthAmerica was also observed. The results of these studies revealed an increasingdiversification of SARS‐CoV‐2 strains. High evolutionary rates and fast populationgrowth characterizes the population dynamics of SARS‐CoV‐2 strains.