Significance We estimate the origin and spread of SARS-CoV-2 in Europe prior to spring 2020 border closures based on viral genome sequences using a phylodynamic model with geographic structure. We confirm that the predominant European outbreak most likely started in Italy and spread from there. This outbreak was probably seeded by a transmission event in either Hubei, China or Germany. In particular, we find that before the first border closures in Europe, the rate of new cases occurring from within-country transmission was within or exceeded the estimated bounds on the rate of new migration cases.