Eukaryotic genomes are organized within the nucleus through interactions with inner nuclear membrane (INM) proteins. How chromatin tethering to the INM is controlled in interphase and how this process contributes to subsequent mitotic nuclear envelope (NE) remodeling remains unclear. We have probed these fundamental questions using the fission yeast Schizosaccharomyces japonicus, which breaks and reforms the NE during mitosis. We show that attachments between heterochromatin and the transmembrane Lem2-Nur1 complex at the INM are remodeled in interphase by the ESCRT-III/Vps4 machinery. Failure of ESCRT-III/Vps4 to release Lem2-Nur1 from heterochromatin leads to persistent association of chromosomes with the INM throughout mitosis. At mitotic exit, such trapping of Lem2-Nur1 on heterochromatin prevents it from re-establishing nucleocytoplasmic compartmentalization. Our work identifies the Lem2-Nur1 complex as a substrate for the nuclear ESCRT machinery and explains how the dynamic tethering of chromosomes to the INM is linked to the establishment of nuclear compartmentalization.