The typical marine animal has increased in biovolume by more than two orders of magnitude since the beginning of the Cambrian, but the causes of this trend remain unknown. We test the hypothesis that the efficiency of intra-organism oxygen delivery is a major constraint on body-size evolution in marine animals. To test this hypothesis, we compiled a dataset comprising 13,723 marine animal genera spanning the Phanerozoic. We coded each genus according to its respiratory medium, circulatory anatomy, and feeding mode. In extant genera, we find that respiratory medium and circulatory anatomy explain more of the difference in size than feeding modes. Likewise, we find that most of the Phanerozoic increase in mean biovolume is accounted for by size increase in taxa that accomplish oxygen delivery through closed circulatory systems. During the Cambrian, water-breathing animals with closed circulatory systems were smaller, on average, than contemporaries with open circulatory systems. However, genera with closed circulatory systems superseded in size genera with open circulatory systems by the Middle Ordovician, as part of their Phanerozoic-long trend of increasing size. In a regression analysis, respiratory and circulatory anatomy explain far more size variation in the living fauna than do feeding modes, even after accounting for taxonomic affinity at the class level. These findings suggest that ecological and environmental drivers of the Phanerozoic increase in the mean size of marine animals operated within strong, anatomically determined constraints.