Upon fertilization, the genome of animal embryos remains transcriptionally inactive until the maternal-to-zygotic transition. At this time, the embryo takes control of its development and transcription begins. How the onset of zygotic transcription is regulated remains unclear. Here, we show that a dynamic competition for DNA binding between nucleosome-forming histones and transcription factors regulates zebrafish genome activation. Taking a quantitative approach, we found that the concentration of non-DNA bound core histones sets the time for the onset of transcription. The reduction in nuclear histone concentration that coincides with genome activation does not affect nucleosome density on DNA, but allows transcription factors to compete successfully for DNA binding. In agreement with this, transcription factor binding is sensitive to histone levels and the concentration of transcription factors also affects the time of transcription. Our results demonstrate that the relative levels of histones and transcription factors regulate the onset of transcription in the embryo.