Biochemical factors can help reprogram somatic cells into pluripotent stem cells, yet the role of biophysical factors during reprogramming is unknown. Here, we show that biophysical cues, in the form of parallel microgrooves on the surface of cell-adhesive substrates, can replace the effects of small-molecule epigenetic modifiers and significantly improve reprogramming efficiency. The mechanism relies on the mechanomodulation of the cells’ epigenetic state. Specifically, decreased histone deacetylase activity and upregulation of the expression of WD repeat domain 5 (WDR5)—a subunit of H3 methyltranferase—by microgrooved surfaces lead to increased histone H3 acetylation and methylation. We also show that microtopography promotes a mesenchymal-to-epithelial transition in adult fibroblasts. Nanofibrous scaffolds with aligned fibre orientation produce effects similar to those produced by microgrooves, suggesting that changes in cell morphology may be responsible for modulation of the epigenetic state. These findings have important implications in cell biology and in the optimization of biomaterials for cell-engineering applications.