Gene regulation in the human genome is controlled by distal enhancers that activate specific nearby promoters1. One model for this specificity is that promoters might have sequence-encoded preferences for certain enhancers, for example mediated by interacting sets of transcription factors or cofactors2. This “biochemical compatibility” model has been supported by observations at individual human promoters and by genome-wide measurements in Drosophila3–9. However, the degree to which human enhancers and promoters are intrinsically compatible has not been systematically measured, and how their activities combine to control RNA expression remains unclear. Here we designed a high-throughput reporter assay called ExP STARR-seq (enhancer x promoter self-transcribing active regulatory region sequencing) and applied it to examine the combinatorial compatibilities of 1,000 enhancer and 1,000 promoter sequences in human K562 cells. We identify simple rules for enhancer-promoter compatibility: most enhancers activated all promoters by similar amounts, and intrinsic enhancer and promoter activities combine multiplicatively to determine RNA output (R2=0.82). In addition, two classes of enhancers and promoters showed subtle preferential effects. Promoters of housekeeping genes contained built-in activating motifs for factors such as GABPA and YY1, which decreased the responsiveness of promoters to distal enhancers. Promoters of variably expressed genes lacked these motifs and showed stronger responsiveness to enhancers. Together, this systematic assessment of enhancer-promoter compatibility suggests a multiplicative model tuned by enhancer and promoter class to control gene transcription in the human genome.