Remdesivir (RDV), a broadly acting nucleoside analogue, is the only FDA approved small molecule antiviral for the treatment of COVID-19 patients. To date, there are no reports identifying SARS-CoV-2 RDV resistance in patients, animal models or in vitro. Here, we selected drug-resistant viral populations by serially passaging SARS-CoV-2 in vitro in the presence of RDV. Using high throughput sequencing, we identified a single mutation in RNA-dependent RNA polymerase (NSP12) at a residue conserved among all coronaviruses in two independently evolved populations displaying decreased RDV sensitivity. Introduction of the NSP12 E802D mutation into our SARS-CoV-2 reverse genetics backbone confirmed its role in decreasing RDV sensitivity in vitro. Substitution of E802 did not affect viral replication or activity of an alternate nucleoside analogue (EIDD2801) but did affect virus fitness in a competition assay. Analysis of the globally circulating SARS-CoV-2 variants (>800,000 sequences) showed no evidence of widespread transmission of RDV-resistant mutants. Surprisingly, we observed an excess of substitutions in spike at corresponding sites identified in the emerging SARS-CoV-2 variants of concern (i.e., H69, E484, N501, H655) indicating that they can arise in vitro in the absence of immune selection. The identification and characterisation of a drug resistant signature within the SARS-CoV-2 genome has implications for clinical management and virus surveillance.