The development of therapeutics to prevent or treat COVID-19 remains an area of intense focus. Protein biologics, including monoclonal antibodies and nanobodies that neutralize virus, have potential for the treatment of active disease. Here, we have used yeast display of a synthetic nanobody library to isolate nanobodies that bind the receptor-binding domain (RBD) of SARS-CoV-2 and neutralize the virus. We show that combining two clones with distinct binding epitopes within the RBD into a single protein construct to generate biparatopic reagents dramatically enhances their neutralizing capacity. Furthermore, the biparatopic nanobodies exhibit enhanced control over clinically relevant RBD variants that escaped recognition by the individual nanobodies. Structural analysis of biparatopic binding to spike (S) protein revealed a unique binding mode whereby the two nanobody paratopes bridge RBDs encoded by distinct S trimers. Accordingly, biparatopic nanobodies offer a way to rapidly generate powerful viral neutralizers with enhanced ability to control viral escape mutants.