Genetic alterations linked to acquired BRAF inhibitor resistance are absent in about 40% of relapsed melanoma patients suggesting the involvement of epigenetic alterations in the development of acquired drug resistance. We investigated epigenetic remodelling in BRAF mutant melanoma upon BRAF/MEK inhibition. An in-vitro model of time dependent transition to acquired drug resistance using mutant BRAF melanoma was used to investigate epigenetic changes following chronic drug exposure. Histone methylation patters were investigated using ChIP-seq, followed by target gene promoter ChIP-PCR and functional verification. A state dependent response to chronic drug treatment was observed. Long term treatment enables the cells to escape the slow cycling state which results in proliferating cellular clusters (drug-tolerant persister colonies) with stem-like characteristics that regain global H3K4me3. Persister colonies are then giving rise to fast proliferating BRAF/MEK inhibitor resistant cells. H3K4me3 ChIP-seq of colonies compared to parental cells revealed differential marking at promotor regions of several target genes involved in MAPKi resistance, including ARAF, BRAF, and CRAF. Two epigenetic modifiers, OGT and TET1 that are both linked to H3K4me3 regulation in embryonic stem cells are highly upregulated in persister colonies and tumour tissue of PDXs from BRAF mutant melanoma patients under MEK1/2 inhibition. shRNA mediated knockdown of OGT and TET1 blocked H3K4me3 increase in IDTC colonies, prevented colony formation and delayed tumour relapse in a BRAF mutant xenograft mouse model. OGT and TET1 mediated epigenetic remodelling through H3K4me3 with upregulation of MAPKi resistant genes is responsible for the emergence of permanent resistance. Both enzymes are promising targets to combat treatment failure and prolong overall survival.