The INO80 chromatin-remodelling complex has been implicated in DNA replication during stress in yeast. However, its role in normal DNA replication and its underlying mechanisms remain unclear. Here, we show that INO80 binds to replication forks and promotes fork progression in human cells under unperturbed, normal conditions. We find that Ino80, which encodes the catalytic ATPase of INO80, is essential for mouse embryonic DNA replication and development. Ino80 is recruited to replication forks through interaction with ubiquitinated H2A-aided by BRCA1-associated protein-1 (BAP1), a tumour suppressor and nuclear de-ubiquitinating enzyme that also functions to stabilize Ino80. Importantly, Ino80 is downregulated in BAP1-defective cancer cells due to the lack of an Ino80 stabilization mechanism via BAP1. Our results establish a role for INO80 in normal DNA replication and uncover a mechanism by which this remodeler is targeted to replication forks, suggesting a molecular basis for the tumour-suppressing function of BAP1.