ATP-dependent chromatin remodellers modulate nucleosome dynamics by mobilizing or disassembling nucleosomes, as well as altering nucleosome composition. These chromatin remodellers generally function by translocating along nucleosomal DNA at the H3–H4 interface of nucleosomes. Here we show that, unlike other remodellers, INO80 translocates along DNA at the H2A–H2B interface of nucleosomes and persistently displaces DNA from the surface of H2A–H2B. DNA translocation and DNA torsional strain created near the entry site of nucleosomes by INO80 promotes both the mobilization of nucleosomes and the selective exchange of H2A.Z–H2B dimers out of nucleosomes and replacement by H2A–H2B dimers without any additional histone chaperones. We find that INO80 translocates and mobilizes H2A.Z-containing nucleosomes more efficiently than those containing H2A, partially accounting for the preference of INO80 to replace H2A.Z with H2A. Our data suggest that INO80 has a mechanism for dimer exchange that is distinct from other chromatin remodellers including its paralogue SWR1.