Allosteric transcription factors (aTFs) have proven widely applicable for biotechnology and synthetic biology as ligand-specific biosensors enabling real-time monitoring, selection and regulation of cellular metabolism. However, both the biosensor specificity and the correlation between ligand concentration and biosensor output signal, also known as the transfer function, often needs to be optimized before meeting application needs. Here, we present a versatile and high-throughput method to evolve prokaryotic aTF specificity and transfer functions in a eukaryote chassis, namely baker's yeast Saccharomyces cerevisiae. From a single round of mutagenesis of the effector-binding domain (EBD) coupled with various toggled selection regimes, we robustly select aTF variants of the cis,cis-muconic acid-inducible transcription factor BenM evolved for change in ligand specificity, increased dynamic output range, shifts in operational range, and a complete inversion-of-function from activation to repression. Importantly, by targeting only the EBD, the evolved biosensors display DNA-binding affinities similar to BenM, and are functional when ported back into a prokaryotic chassis. The developed platform technology thus leverages aTF evolvability for the development of new host-agnostic biosensors with user-defined small-molecule specificities and transfer functions.