Zygotic genome activation (ZGA) is a major genome programming event whereby the cells of the embryo begin to adopt specified fates. Experiments in Drosophila and zebrafish have revealed that ZGA depends on transcription factors that provide large-scale control of gene expression by direct and specific binding to gene regulatory sequences. Zelda (Zld) plays such a role in the Drosophila embryo, where it has been shown to control the action of patterning signals; however, the mechanisms underlying this effect remain largely unclear. A recent model proposed that Zld binding sites act as quantitative regulators of the spatiotemporal expression of genes activated by Dorsal (Dl), the morphogen that patterns the dorsoventral axis. Here we tested this model experimentally, using enhancers of brinker (brk) and short gastrulation (sog), both of which are directly activated by Dl, but at different concentration thresholds. In agreement with the model, we show that there is a clear positive correlation between the number of Zld binding sites and the spatial domain of enhancer activity. Likewise, the timing of expression could be advanced or delayed. We present evidence that Zld facilitates binding of Dl to regulatory DNA, and that this is associated with increased chromatin accessibility. Importantly, the change in chromatin accessibility is strongly correlated with the change in Zld binding, but not Dl. We propose that the ability of genome activators to facilitate readout of transcriptional input is key to widespread transcriptional induction during ZGA.