Respiratory viruses such as SARS-CoV-2, influenza, and respiratory syncytial virus (RSV) represent pressing health risks. Rapid diagnostic tests for these viruses detect single antigens or nucleic acids, which do not necessarily correlate with the amount of the intact virus. Instead, specific detection of intact respiratory virus particles may be more effective at assessing the contagiousness of a patient. Here, we report GLOVID, a modular biosensor platform to detect intact virions against a background of "free" viral proteins in solution. Our approach harnesses the multivalent display of distinct proteins on the surface of a viral particle to template the reconstitution of a split luciferase, allowing specific, single-step detection of intact influenza A and RSV virions corresponding to 0.1-0.3 fM of genomic units. The protein ligation system used to assemble GLOVID sensors is compatible with a broad range of binding domains, including nanobodies, scFv fragments, and cyclic peptides, which allows straightforward adjustment of the sensor platform to target different viruses.