Multiple SARS-CoV-2 introductions have been detected in Spain, and at least four resulted in the emergence of locally transmitted clusters that originated not later than mid-February, with further dissemination to many other countries around the world, and a few weeks before the explosion of COVID-19 cases detected in Spain during the first week of March. The majority of the earliest variants detected in Spain branched in the clade 19B (D614 viruses), which was the most prevalent clade during the first weeks of March, pointing to a founder effect. However, from mid-March to June 2020, G614-bearing viruses (clades 20A, 20B, and 20C) overcame D614 variants in Spain, probably as a consequence of an evolutionary advantage of this substitution in the spike protein. A higher infectivity of G614-bearing viruses than D614 variants was detected, suggesting that this substitution in SARS-CoV-2 spike protein could be behind the variant shift observed in Spain.