In this study, the full length genomes of two SARS-CoV-2 strains (EPI_ISL_412973 and EPI_ISL_412974) isolated in Italy, one from an Italian patient, the other from a Chinese tourist visiting Rome, are completely sequenced and analysed, after virus cultivation. Compared to the viral genome sequence of the COVID-19 patient in Wuhan, the sequence from the Chinese tourist had two nt differences, while that of the Italian patient had four. Phylogenetic analysis consistently placed the Italian patient’s strain in a distinct cluster from the tourist’s strain. The strain of the Italian patient grouped with other viral strains identified in Germany and Mexico, while the strain from the Chinese tourist, related with the Wuhan virus strain, clustered with different European strains and a strain from Australia. Other sequences from strains collected in Europe, which were included in the phylogenetic analysis, ended up in separate clusters from the ones respectively containing the sequences of the two patients reported here. The results are consistent with several introductions of SARS-CoV-2 in Europe and/or further circulation of the single strain originating in Wuhan with concurrent evolution and accumulation of mutations. The mutations found in the virus identified in Lombardy, compared with the reference Wuhan strain, and the identification of amino acids changes, should be further investigated to understand whether they may affect virus characteristics. Some limitations need be mentioned: first, the lack of epidemiological information available with most sequences deposited in the database; second, the number of genomes available at the time of the analysis and consequently their selection. Nevertheless, these data may be useful to understand the dynamics of the local transmission of SARS-CoV-2 in Europe.