Savanna systems exhibit a high plant functional diversity. While aridity and livestock grazing intensity have been widely discussed as drivers of savanna vegetation composition, physical soil properties have received less attention. Since savannas can show local differences in soil properties, these might act as environmental filters and affect plant diversity and ecosystem functioning at the patch scale. However, research on the link between savanna vegetation diversity and ecosystem function is widely missing. In this study, we aim at understanding the impact of local heterogeneity in soil conditions on plant diversity and on ecosystem functions. For this, we used the ecohydrological savanna model EcoHyD. The model simulates the fate of multiple plant functional types and their interactions with local biotic and abiotic conditions. We applied the model to a set of different landscapes under a wide range of livestock grazing and precipitation scenarios to assess the impact of local heterogeneity in soil conditions on the composition and diversity of plant functional types and on ecosystem functions. Comparisons between homogeneous and heterogeneous landscapes revealed that landscape soil heterogeneity allowed for a higher functional diversity of vegetation under conditions of high competition, i.e. scenarios of low grazing stress. However, landscape heterogeneity did not have this effect under low grazing stress in combination with high mean annual precipitation. Further, landscape heterogeneity led to a higher community biomass, especially for lower rainfall conditions, but also dependent on grazing stress. Total transpiration of the plant community decreased in heterogeneous landscapes under arid conditions. This study highlights that local soil conditions interact with precipitation and grazing in driving savanna vegetation. It clearly shows that vegetation diversity and resulting ecosystem functioning can be driven by landscape heterogeneity. We therefore suggest that future research on ecosystem functioning of savanna systems should focus on the links between local environmental conditions via plant functional diversity to ecosystem functioning.