Coronavirus disease 2019 (COVID-19) was first diagnosed in Scotland on 1 March 2020. During the first month of the outbreak, 2,641 cases of COVID-19 led to 1,832 hospital admissions, 207 intensive care admissions and 126 deaths. We aimed to identify the source and number of introductions of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) into Scotland using a combined phylogenetic and epidemiological approach. Sequencing of 1,314 SARS-CoV-2 viral genomes from available patient samples enabled us to estimate that SARS-CoV-2 was introduced to Scotland on at least 283 occasions during February and March 2020. Epidemiological analysis confirmed that early introductions of SARS-CoV-2 originated from mainland Europe (the majority from Italy and Spain). We identified subsequent early outbreaks in the community, within healthcare facilities and at an international conference. Community transmission occurred after 2 March, 3 weeks before control measures were introduced. Earlier travel restrictions or quarantine measures, both locally and internationally, would have reduced the number of COVID-19 cases in Scotland. The risk of multiple reintroduction events in future waves of infection remains high in the absence of population immunity.