Stroke patients frequently display spatial neglect, an inability to report, or respond to, relevant stimuli in the contralesional space. Although this syndrome is widely considered to result from the dysfunction of a large-scale attention network, the individual contributions of damaged grey and white matter regions to neglect are still being disputed. Moreover, while the neuroanatomy of neglect in right hemispheric lesions is well studied, the contributions of left hemispheric brain regions to visuospatial processing are less well understood. To address this question, 128 left hemisphere acute stroke patients were investigated with respect to left- and rightward spatial biases measured as severity of deviation in the line bisection test and as Center of Cancellation (CoC) in the Bells Test. Causal functional contributions and interactions of nine predefined grey and white matter regions of interest in visuospatial processing were assessed using Multi-perturbation Shapley value Analysis (MSA). MSA, an inference approach based on game theory, constitutes a robust and exact multivariate mathematical method for inferring functional contributions from multi-lesion patterns. According to the analysis of performance in the Bells test, leftward attentional bias (contralesional deficit) was associated with contributions of the left superior temporal gyrus and rightward attentional bias with contributions of the left inferior parietal lobe, whereas the arcuate fascicle was contributed to both contra- and ipsilesional bias. Leftward and rightward deviations in the line bisection test were related to contributions of the superior longitudinal fascicle and the inferior parietal lobe, correspondingly. Thus, Bells test and line bisection tests, as well as ipsi- and contralesional attentional biases in these tests, have distinct neural correlates. Our findings demonstrate the contribution of different grey and white matter structures to contra- and ipsilesional spatial biases as revealed by left hemisphere stroke. The results provide new insights into the role of the left hemisphere in visuospatial processing.