Glaucoma and other optic neuropathies affect millions of people worldwide, ultimately causing progressive and irreversible degeneration of retinal ganglion cells (RGCs) and blindness. Previous research into cell replacement therapy of these neurodegenerative diseases has been stalled due to the incapability for grafted RGCs to integrate into the retina and project properly along the long visual pathway. RGC regeneration would be a promising alternative approach but mammalian retinas lack regenerative capacity. It therefore has long been a great challenge to regenerate functional and properly projecting RGCs for vision restoration in mammals. Here we show that the transcription factors (TFs) Math5 and Brn3b together are able to reprogram mature mouse Müller glia (MG) into RGCs. The reprogrammed RGCs extend long axons that make appropriate intra-retinal and extra-retinal projections through the entire visual pathway to innervate both image-forming and non-image-forming brain targets. They exhibit typical neuronal electrophysiological properties and improve visual responses in RGC loss mouse models. Together, our data provide evidence that mammalian MG can be reprogrammed by defined TFs to achieve regeneration of functional RGCs as well as a promising new therapeutic approach to restore vision to patients with glaucoma and other optic neuropathies.