Full genome sequences are increasingly used to track the geographic spread and transmission dynamics of viral pathogens. Here, with a focus on Israel, we sequence 212 SARS-CoV-2 sequences and use them to perform a comprehensive analysis to trace the origins and spread of the virus. We find that travelers returning from the United States of America significantly contributed to viral spread in Israel, more than their proportion in incoming infected travelers. Using phylodynamic analysis, we estimate that the basic reproduction number of the virus was initially around 2.5, dropping by more than two-thirds following the implementation of social distancing measures. We further report high levels of transmission heterogeneity in SARS-CoV-2 spread, with between 2-10% of infected individuals resulting in 80% of secondary infections. Overall, our findings demonstrate the effectiveness of social distancing measures for reducing viral spread.