Population pharmacokinetic (PopPK) models are vital for decision making across the drug development lifecycle; however, conventional model development is labour-intensive and time-consuming. In this paper, we present an approach to automatically develop popPK model structures for extravascularly administered drugs using optimisation algorithms. We propose a generic parameter space for generating model structures and a penalty function for selecting the optimal configurations. Across four clinical datasets we observed the reproducible discovery of models comparable with those manually developed with an average search time under 48 hours. These results demonstrate that a single penalty function and model space can be used within an optimisation framework to automatically identify model structures for a diverse range of drugs. Adoption of automatic model search can accelerate popPK analysis, improve model quality, increase reproducibility, and reduce manual effort for modellers.