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The vaccination roll-out of the COVID-19 vaccines in Israel has been highly successful. By February 9th, approximately 39% of the population has already been administered at least one dose of the BNT162b2 vaccine. Efforts to estimate the true real-world effectiveness of the vaccine have been hampered by disease dynamics and social-economic discrepancies. Here, using counts of positive and hospitalized cases of vaccinated individuals, we conduct a sensitive analysis of the vaccine effectiveness. Under an assumption of no effectiveness on the first two weeks after the 1^st dose, the analysis shows effectiveness of 72% in reducing SARS-CoV-2 positive cases (symptomatic and asymptomatic), 83% reduction of COVID-19 hospitalizations and 86% reduction in severe cases in 60 years and older individuals the second week after the 2^nd dose. On weeks 3-4 after the 2^nd dose, we observe vaccine effectiveness of 95%+, however cases may still accumulate. Our analysis suggests that high effectiveness of the vaccine only starts after three weeks, which coincides with the administration of the 2^nd dose. As more granular data will be available, it will be possible to extract more exact estimates; however, the emerging evidence suggest that the vaccine is highly effective in reducing cases, hospitalizations and deaths.