SARS-CoV-2 evolution threatens vaccine- and natural infection-derived immunity as well as the efficacy of therapeutic antibodies. To improve public health preparedness, we sought to predict which existing amino acid mutations in SARS-CoV-2 might contribute to future variants of concern. We tested the predictive value of features comprising epidemiology, evolution, immunology, and neural network-based protein sequence modeling, and identified primary biological drivers of SARS-CoV-2 intra-pandemic evolution. We found evidence that ACE2-mediated transmissibility and resistance to population-level host immunity has waxed and waned as a primary driver of SARS-CoV-2 evolution over time. We retroactively identified with high accuracy (area under the receiver operator characteristic curve, AUROC=0.92-0.97) mutations that will spread, at up to four months in advance, across different phases of the pandemic. The behavior of the model was consistent with a plausible causal structure wherein epidemiological covariates combine the effects of diverse and shifting drivers of viral fitness. We applied our model to forecast mutations that will spread in the future and characterize how these mutations affect the binding of therapeutic antibodies. These findings demonstrate that it is possible to forecast the driver mutations that could appear in emerging SARS-CoV-2 variants of concern. We validate this result against Omicron, showing elevated predictive scores for its component mutations prior to emergence, and rapid score increase across daily forecasts during emergence. This modeling approach may be applied to any rapidly evolving pathogens with sufficiently dense genomic surveillance data, such as influenza, and unknown future pandemic viruses.