During DNA replication, chromatin must be disassembled and faithfully reassembled on newly synthesized genomes. The mechanisms that govern the assembly of chromatin structures following DNA replication are poorly understood. Here, we exploited Okazaki fragment synthesis and other assays to study how nucleosomes are deposited and become organized in S. cerevisiae. We observe that global nucleosome positioning is quickly established on newly synthesized DNA in vivo. Importantly, we find that ATP-dependent chromatin-remodeling enzymes, Isw1 and Chd1, collaborate with histone chaperones to remodel nucleosomes as they are loaded behind a replication fork. Using a whole-genome sequencing approach, we determine that the positioning of newly deposited nucleosomes in vivo is specified by the combined actions of ATP-dependent chromatin-remodeling enzymes and select DNA-binding proteins. Altogether, our data provide in vivo evidence for coordinated "loading and remodeling" of nucleosomes behind the replication fork, allowing for rapid organization of chromatin during S phase.