The eukaryotic replisome is a molecular machine that coordinates the Cdc45-MCM-GINS (CMG) replicative DNA helicase with DNA polymerases α, δ, and ε and other proteins to copy the leading- and lagging-strand templates at rates between 1 and 2 kb min⁻¹. We have now reconstituted this sophisticated machine with purified proteins, beginning with regulated CMG assembly and activation. We show that replisome-associated factors Mrc1 and Csm3/Tof1 are crucial for in vivo rates of replisome progression. Additionally, maximal rates only occur when DNA polymerase ε catalyzes leading-strand synthesis together with its processivity factor PCNA. DNA polymerase δ can support leading-strand synthesis, but at slower rates. DNA polymerase δ is required for lagging-strand synthesis, but surprisingly also plays a role in establishing leading-strand synthesis, before DNA polymerase ε engagement. We propose that switching between these DNA polymerases also contributes to leading-strand synthesis under conditions of replicative stress.