The camera can be traced back many years ago, so it is hard to say who the first person was to actually discover how to make a proper camera. Cameras were slowly developed from a camera obscura, a device that projected an image onto paper.
However the first person to produce a device that actually made a photograph was a man named Nicephore Niepce, and this was in 1816.
His photograph was not completely successful though as the image he produced would only last a while before the whole paper darkened due to its exposure to light. It could be said though that this man was the one that discovered the first camera and it was his device that was developed to make the cameras that we have today.
Photographic film was developed by George Eastman. The camera that he created he called a 'Kodak' which to this day is a well known camera brand, some would say it was Eastman who discovered the modern camera.
It was Eatman's development of the camera that made it widely available to the public as well, because the technology then became available at quite a cheap price, once mass production was a possibility.