Both genome-wide genetic and epigenetic alterations are fundamentally important for the development of cancers, but the interdependence of these aberrations is poorly understood. Glioblastomas and other cancers with the CpG island methylator phenotype (CIMP) constitute a subset of tumours with extensive epigenomic aberrations and a distinct biology. Glioma CIMP (G-CIMP) is a powerful determinant of tumour pathogenicity, but the molecular basis of G-CIMP remains unresolved. Here we show that mutation of a single gene, isocitrate dehydrogenase 1 (IDH1), establishes G-CIMP by remodelling the methylome. This remodelling results in reorganization of the methylome and transcriptome. Examination of the epigenome of a large set of intermediate-grade gliomas demonstrates a distinct G-CIMP phenotype that is highly dependent on the presence of IDH mutation. Introduction of mutant IDH1 into primary human astrocytes alters specific histone marks, induces extensive DNA hypermethylation, and reshapes the methylome in a fashion that mirrors the changes observed in G-CIMP-positive lower-grade gliomas. Furthermore, the epigenomic alterations resulting from mutant IDH1 activate key gene expression programs, characterize G-CIMP-positive proneural glioblastomas but not other glioblastomas, and are predictive of improved survival. Our findings demonstrate that IDH mutation is the molecular basis of CIMP in gliomas, provide a framework for understanding oncogenesis in these gliomas, and highlight the interplay between genomic and epigenomic changes in human cancers.