They say the findings could help treat blindness, caused by glaucoma, if similar results can be repeated in humans.
The study, published in the journal Stem Cells Translational Medicine, used the cells to form new nerves in the eye.
These hooked up with the existing nerves, restoring sight.
Glaucoma can lead to blindness and is caused by a build-up of pressure within the eye. This kills retinal ganglion cells, the nerves which take information from the retina and pass it onto the brain.
Researchers at University College London and Moorfields Eye Hospital believe they have regenerated the retinal ganglion cells using human stem cells.
With permission from families, cell samples were taken from eyes which had been donated for cornea transplants.
Very rare cells in the eye, Muller glia stem cells, were collected. These were grown in the laboratory and converted into retinal ganglion cells.
These cells were then transplanted into the eyes of rats without retinal ganglion cells. Before the transplant the rats were blind. Afterwards, electrodes attached to the rats' heads showed that their brains were responding to low levels of light.
One of the researchers Dr Astrid Limb said the new cells were not joining up with the optic nerve as they would normally. Instead they appeared to be "bridging" with other nerves in the retina, which could pass the message on.
She said: "Although this research is still a long way from the clinic, it is a significant step towards our ultimate goal of finding a cure for glaucoma and other related conditions."