Assignment of resonances of nuclear magnetic resonance (NMR) spectra to specific atoms within a protein remains a labor-intensive and challenging task. Automation of the assignment process often remains a bottleneck in the exploitation of solution NMR spectroscopy for the study of protein structure-dynamics-function relationships. We present an approach to the assignment of backbone triple resonance spectra of proteins. A Bayesian statistical analysis of predicted and observed chemical shifts is used in conjunction with inter-spin connectivities provided by triple resonance spectroscopy to calculate a pseudo-energy potential that drives a simulated annealing search for the most optimal set of resonance assignments. Termed Bayesian Assisted Assignments by Simulated Annealing (BARASA), a C++ program implementation is tested against systems ranging in size to over 450 amino acids including examples of intrinsically disordered proteins. BARASA is fast, robust, accommodates incomplete and incorrect information, and outperforms current algorithms – especially in cases of sparse data and is sufficiently fast to allow for real-time evaluation during data acquisition.