Rhinoviruses (RVs) are the pathogens most often responsible for the common cold, and are a frequent cause of exacerbations in asthma, chronic obstructive pulmonary disease and cystic fibrosis. Here we report the discovery of IMP-1088, a picomolar dual inhibitor of the human N-myristoyltransferases NMT1 and NMT2, and use it to demonstrate that pharmacological inhibition of host-cell N-myristoylation rapidly and completely prevents rhinoviral replication without inducing cytotoxicity. The identification of cooperative binding between weak-binding fragments led to rapid inhibitor optimization through fragment reconstruction, structure-guided fragment linking and conformational control over linker geometry. We show that inhibition of the co-translational myristoylation of a specific virus-encoded protein (VP0) by IMP-1088 potently blocks a key step in viral capsid assembly, to deliver a low nanomolar antiviral activity against multiple RV strains, poliovirus and foot and-mouth disease virus, and protection of cells against virus-induced killing, highlighting the potential of host myristoylation as a drug target in picornaviral infections.