Despite transformative advances in protein design with deep learning, the design of small-molecule-binding proteins and sensors for arbitrary ligands remains a grand challenge. Here we combine deep learning and physics-based methods to generate a family of proteins with diverse and designable pocket geometries, which we employ to computationally design binders for six chemically and structurally distinct small-molecule targets. Biophysical characterization of the designed binders revealed nanomolar to low micromolar binding affinities and atomic-level design accuracy. The bound ligands are exposed at one edge of the binding pocket, enabling the de novo design of chemically induced dimerization (CID) systems; we take advantage of this to create a biosensor with nanomolar sensitivity for cortisol. Our approach provides a general method to design proteins that bind and sense small molecules for a wide range of analytical, environmental, and biomedical applications.