Objectives. SARS-CoV-2 whole-genome analysis has identified three large clades spreading worldwide, designated G, V and S. This study aims to analyze the diffusion of SARS-CoV-2 in Spain/Europe. Methods. Maximum likelihood phylogenetic and Bayesian phylodynamic analyses have been performed to estimate the most probable temporal and geographic origin of different phylogenetic clusters and the diffusion pathways of SARS-CoV-2. Results. Phylogenetic analyses of the first 28 SARS-CoV-2 whole genome sequences obtained from patients in Spain revealed that most of them are distributed in G and S clades (13 sequences in each) with the remaining two sequences branching in the V clade. Eleven of the Spanish viruses of the S clade and six of the G clade grouped in two different monophyletic clusters (S-Spain and G-Spain, respectively), with the S-Spain cluster also comprising 8 sequences from 6 other countries from Europe and the Americas. The most recent common ancestor (MRCA) of the SARS-CoV-2 pandemic was estimated in the city of Wuhan, China, around November 24, 2019, with a 95% highest posterior density (HPD) interval from October 30-December 17, 2019. The origin of S-Spain and G-Spain clusters were estimated in Spain around February 14 and 18, 2020, respectively, with a possible ancestry of S-Spain in Shanghai. Conclusions. Multiple SARS-CoV-2 introductions have been detected in Spain and at least two resulted in the emergence of locally transmitted clusters, with further dissemination of one of them to at least 6 other countries. These results highlight the extraordinary potential of SARS-CoV-2 for rapid and widespread geographic dissemination.