Natural and engineered genetic systems require the coordinated expression of proteins. In bacteria, translational coupling provides a genetically encoded mechanism to control expression level ratios within multi-cistronic operons. We have developed a sequence-to-function biophysical model of translational coupling to predict expression level ratios in natural operons and to design synthetic operons with desired expression level ratios. To quantitatively measure ribosome re-initiation rates, we designed and characterized 22 bi-cistronic operon variants with systematically modified intergenic distances and upstream translation rates. We then derived a thermodynamic free energy model to calculate de novo initiation rates as a result of ribosome-assisted unfolding of intergenic RNA structures. The complete biophysical model has only five free parameters, but was able to accurately predict downstream translation rates for 120 synthetic bi-cistronic and tri-cistronic operons with rationally designed intergenic regions and systematically increased upstream translation rates. The biophysical model also accurately predicted the translation rates of the nine protein atp operon, compared to ribosome profiling measurements. Altogether, the biophysical model quantitatively predicts how translational coupling controls protein expression levels in synthetic and natural bacterial operons, providing a deeper understanding of an important post-transcriptional regulatory mechanism and offering the ability to rationally engineer operons with desired behaviors.