Living tissue and extracellular matrices possess viscoelastic properties, but understanding how viscoelastic matrix regulates chromatin and the epigenome is limited. Here, we find that the regulation of the epigenetic state by the viscoelastic matrix is more pronounced on softer matrices. Cells on viscoelastic matrices exhibit larger nuclei, increased nuclear lamina ruffling, loosely organized chromatin, and faster chromatin dynamics, compared to those on elastic matrices. These changes are accompanied by a global increase in euchromatic marks and a local increase in chromatin accessibility at the cis -regulatory elements associated with neuronal and pluripotent genes. Consequently, viscoelastic matrices enhanced the efficiency of reprogramming fibroblasts into neurons and induced pluripotent stem cells, respectively. Together, our findings demonstrate the key roles of matrix viscoelasticity in the regulation of epigenetic state, and uncover a new mechanism of biophysical regulation of chromatin and cell reprogramming, with implications for the design of smart materials to engineer cell fate.