Epistatic interactions determine the phenotypic consequences of mutations and shape the course of evolution. However, little is known about the pattern of epistatic interactions among the possible mutations within a protein and the extent and temporal dynamics with which the effects of mutations change during evolution. By using a novel method to analyze experimental mutational datasets, I show that the architecture of epistatic interactions within a protein is surprisingly simple: Knowing only the context-independent effects and pairwise interactions of amino acids is sufficient to predict the phenotype with high accuracy. I then combine ancestral protein reconstruction with deep mutational scanning to experimentally reconstruct how the effect of every possible point mutation in a protein changed during long-term evolution. The effects of most mutations changed gradually and randomly at a rate characteristic to each mutation—a pattern I call epistatic drift. Epistatic drift randomized the effects of most mutations during evolution, making the outcome of evolution highly unpredictable. The statistical regularity of epistatic drift, however, means that this unpredictability can be quantified: A probability distribution for the future effect of a mutation—therefore the timescale at which evolution becomes unpredictable—can be calculated from the rate of epistatic drift. Overall, my work reveals a simple architecture and statistical regularity of epistasis and demonstrates the pervasive historical contingency of protein evolution.