The shape and size of the human cell nucleus is highly variable amongst cell types and tissues. Changes in nuclear morphology are associated with disease, including cancer, as well as with premature and normal aging. Despite the very fundamental nature of nuclear morphology, the cellular factors that determine nuclear shape and size are not well understood. To identify regulators of nuclear architecture in a systematic and unbiased fashion, we performed a high-throughput imaging-based siRNA screen targeting 867 nuclear proteins including chromatin-associated proteins, epigenetic regulators, and nuclear envelope components. Using multiple morphometric parameters and eliminating cell cycle effectors, we identified a set of novel determinants of nuclear size and shape. Interestingly, most identified factors altered nuclear morphology without affecting the levels of lamin proteins, which are known prominent regulators of nuclear shape. In contrast, a major group of nuclear shape regulators were modifiers of repressive heterochromatin. Biochemical and molecular analysis uncovered a direct physical interaction of histone H3 with lamin A mediated via combinatorial histone modifications. Furthermore, disease-causing lamin A mutations that result in disruption of nuclear shape inhibited lamin A-histone H3 interactions. Finally, oncogenic histone H3.3 mutants defective for H3K27 methylation resulted in nuclear morphology abnormalities. Altogether, our results represent a systematic exploration of cellular factors involved in determining nuclear morphology and they identify the interaction of lamin A with histone H3 as an important contributor to nuclear morphology in human cells.