Since the discovery of induced pluripotent stem cells (iPSCs), numerous approaches have been explored to improve the original protocol, which is based on a two-dimensional (2D) cell-culture system. Surprisingly, nothing is known about the effect of a more biologically faithful 3D environment on somatic-cell reprogramming. Here, we report a systematic analysis of how reprogramming of somatic cells occurs within engineered 3D extracellular matrices. By modulating microenvironmental stiffness, degradability and biochemical composition, we have identified a previously unknown role for biophysical effectors in the promotion of iPSC generation. We find that the physical cell confinement imposed by the 3D microenvironment boosts reprogramming through an accelerated mesenchymal-to-epithelial transition and increased epigenetic remodelling. We conclude that 3D microenvironmental signals act synergistically with reprogramming transcription factors to increase somatic plasticity.