Chromosome replication is performed by a complex and intricate ensemble of proteins termed the replisome, where the DNA polymerases Polδ and Polε, DNA polymerase α-primase (Polα) and accessory proteins including AND-1, CLASPIN and TIMELESS-TIPIN (respectively known as Ctf4, Mrc1 and Tof1-Csm3 in Saccharomyces cerevisiae) are organized around the CDC45-MCM-GINS (CMG) replicative helicase. Because a functional human replisome has not been reconstituted from purified proteins, how these factors contribute to human DNA replication and whether additional proteins are required for optimal DNA synthesis are poorly understood. Here we report the biochemical reconstitution of human replisomes that perform fast and efficient DNA replication using 11 purified human replication factors made from 43 polypeptides. Polε, but not Polδ, is crucial for optimal leading-strand synthesis. Unexpectedly, Polε-mediated leading-strand replication is highly dependent on the sliding-clamp processivity factor PCNA and the alternative clamp loader complex CTF18-RFC. We show how CLASPIN and TIMELESS-TIPIN contribute to replisome progression and demonstrate that, in contrast to the budding yeast replisome, AND-1 directly augments leading-strand replication. Moreover, although AND-1 binds to Polα, the interaction is dispensable for lagging-strand replication, indicating that Polα is functionally recruited via an AND-1-independent mechanism for priming in the human replisome. Collectively, our work reveals how the human replisome achieves fast and efficient leading-strand and lagging-strand DNA replication, and provides a powerful system for future studies of the human replisome and its interactions with other DNA metabolic processes.