The detailed positions of nucleosomes profoundly impact gene regulation and are partly encoded by the genomic DNA sequence. However, less is known about the functional consequences of this encoding. Here, we address this question using a genome-wide map of approximately 380,000 yeast nucleosomes that we sequenced in their entirety. Utilizing the high resolution of our map, we refine our understanding of how nucleosome organizations are encoded by the DNA sequence and demonstrate that the genomic sequence is highly predictive of the in vivo nucleosome organization, even across new nucleosome-bound sequences that we isolated from fly and human. We find that Poly(dA:dT) tracts are an important component of these nucleosome positioning signals and that their nucleosome-disfavoring action results in large nucleosome depletion over them and over their flanking regions and enhances the accessibility of transcription factors to their cognate sites. Our results suggest that the yeast genome may utilize these nucleosome positioning signals to regulate gene expression with different transcriptional noise and activation kinetics and DNA replication with different origin efficiency. These distinct functions may be achieved by encoding both relatively closed (nucleosome-covered) chromatin organizations over some factor binding sites, where factors must compete with nucleosomes for DNA access, and relatively open (nucleosome-depleted) organizations over other factor sites, where factors bind without competition.