A ubiquitous feature of eukaryotic transcriptional regulation is cooperative self-assembly between transcription factors (TFs) and DNA cis-regulatory motifs. It is thought that this strategy enables specific regulatory connections to be formed in gene networks between otherwise weakly interacting, low-specificity molecular components. Here, using synthetic gene circuits constructed in yeast, we find that high regulatory specificity can emerge from cooperative, multivalent interactions among artificial zinc-finger-based TFs. We show that circuits “wired” using the strategy of cooperative TF assembly are effectively insulated from aberrant misregulation of the host cell genome. As we demonstrate in experiments and mathematical models, this mechanism is sufficient to rescue circuit-driven fitness defects, resulting in genetic and functional stability of circuits in long-term continuous culture. Our naturally inspired approach offers a simple, generalizable means for building high-fidelity, evolutionarily robust gene circuits that can be scaled to a wide range of host organisms and applications.