Foreign investors have acquired approximately 90 million hectares of land for agriculture over the past two decades. The effects of these investments on local food security remain unknown. While additional cropland and intensified agriculture could potentially increase crop production, preferential targeting of prime agricultural land and transitions toward export-bound crops might affect local access to nutritious foods. We test these hypotheses in a global systematic analysis of the food security implications of existing land concessions. We combine agricultural, remote sensing, and household survey data (available in 11 sub-Saharan African countries) with georeferenced information on 160 land acquisitions in 39 countries. We find that the intended changes in cultivated crop types generally imply transitions toward energy-rich, but nutrient-poor, crops that are predominantly destined for export markets. Specific impacts on food production and access vary substantially across regions. Deals likely have little effect on food security in eastern Europe and Latin America, where they predominantly occur within agricultural areas with current export-oriented crops, and where agriculture would have both expanded and intensified regardless of the land deals. This contrasts with Asia and sub-Saharan Africa, where deals are associated with both an expansion and intensification (in Asia) of crop production. Deals in these regions also shift production away from local staples and coincide with a gradually decreasing dietary diversity among the surveyed households in sub-Saharan Africa. Together, these findings point to a paradox, where land deals can simultaneously increase crop production and threaten local food security.