Purpose The purpose of this paper is to analyse the institutional threshold effects of foreign aid on foreign direct investment (FDI). Design/methodology/approach This paper develops a theoretical model from an extended Solow model that introduces the conductive effect of institutions in an aid recipient country towards the capacity of attracting FDI. This study evidences threshold effects with the most recent panel threshold models that consider endogeneity issues. The data on economic institutions and foreign aid are decomposed into disaggregated level to reveal the detailed threshold pattern. Several sample subsets are used for a heterogeneity analysis. Findings Conducting empirical research on a sample of 62 countries during the period 2003–2016, this study finds robust evidence of the existence of an institutional threshold in the aid–FDI nexus which a country must attain to reap the full attraction of FDI by foreign aid providing financial resources. Furthermore, foreign aid tends to promote FDI in institutions characterized by a right-sized government, a strengthened legal system and an appropriate regulatory environment. On the other hand, aid may crowd out FDI. The results are robust to regional combinations and a subset of low and lower-middle-income countries. In addition, this study finds that aid targeted at social infrastructure and services has a positive effect regardless of institutional threshold. Originality/value This paper contributes to the literature by introducing a non-linear and discontinuous effect of aid on FDI, i.e. a threshold effect, highlighting the relevance of legal systems and regulations and the possibility of a crowding-out effect on FDI for specific institutional regimes. The thresholds provide a guide for donor countries to ensure aid effectiveness at the risk of being counterproductive and for recipient countries to better assess the institutional dimensions that need to be improved.