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Background: The timing of SARS-CoV-2 transmission is a critical factor to understand the epidemic trajectory and the impact of isolation, contact tracing and other non-pharmaceutical interventions on the spread of COVID-19 epidemics. Methods: We examined the distribution of transmission event times with respect to exposure and onset of symptoms. We analysed 119 transmission pairs with known date of onset of symptoms for both index and secondary cases and partial information on their intervals of exposure. We inferred the distribution for generation time and time from onset of symptoms to transmission by maximum likelihood. We modelled different relations between time of infection, onset of symptoms and transmission, inferring the most appropriate one according to the Akaike Information Criterion. Finally, we estimated the fraction of pre-symptomatic and early symptomatic transmissions among all pairs using a Bayesian approach. Findings: For symptomatic individuals, the timing of transmission of SARS-CoV-2 was more directly linked to the onset of clinical symptoms of COVID-19 than to the time since infection. The time of transmission was approximately centered and symmetric around the onset of symptoms, with three quarters of events occurring in the window from 2-3 days before to 2-3 days after. The pre-symptomatic infectious period extended further back in time for individuals with longer incubation periods. Overall, the fraction of transmission from strictly pre-symptomatic infections was high (41%; 95%CI 31-50%), but a comparably large fraction of transmissions occurred on the same day as the onset of symptoms or the next day (35%; 95%CI 26-45%). We caution against overinterpretation of the fraction and timing of late symptomatic transmissions, due to their dependence on behavioural factors and interventions. Interpretation: Infectiousness is causally driven by the onset of symptoms. Public health authorities should reassess their policies on the contact tracing window in the light of individual variability in presymptomatic infectious period. Information about when a case was infected should be collected where possible, in order to assess how far into the past their contacts should be traced. The large fraction of transmission from strictly pre-symptomatic infections limits the efficacy of symptom-based interventions, while the large fraction of early symptomatic transmissions underlines the critical importance of individuals distancing themselves from others as soon as they notice any symptoms, even if mild. Rapid or at-home testing and contextual risk information could greatly facilitate efficient early isolation. Funding Statement: The study was funded by an award from the Li Ka Shing Foundation to CF. Declaration of Interests: None of the authors have competing financial or non-financial interests.