Methods to automate structure elucidation that can be applied broadly across chemical structure space have the potential to greatly accelerate chemical discovery. NMR spectroscopy is the most widely used and arguably the most powerful method for elucidating structures of organic molecules. Here we introduce a machine learning (ML) framework that provides a quantitative probabilistic ranking of the most likely structural connectivity of an unknown compound when given routine, experimental one dimensional ¹H and/or ¹³C NMR spectra. In particular, our ML-based algorithm takes input NMR spectra and (i) predicts the presence of specific substructures out of hundreds of substructures it has learned to identify; (ii) annotates the spectrum to label peaks with predicted substructures; and (iii) uses the substructures to construct candidate constitutional isomers and assign to them a probabilistic ranking. Using experimental spectra and molecular formulae for molecules containing up to 10 non-hydrogen atoms, the correct constitutional isomer was the highest-ranking prediction made by our model in 67.4% of the cases and one of the top-ten predictions in 95.8% of the cases. This advance will aid in solving the structure of unknown compounds, and thus further the development of automated structure elucidation tools that could enable the creation of fully autonomous reaction discovery platforms.