The hidden self-portrait was on the back of another of the artist's early paintings, "Head of a Peasant Woman", and was hidden under layers of glue and cardboard.
It was discovered when the painting, which has been in the museum's collections since 1960, was to be x-rayed before an exhibition.
The museum's curator Lesley Stevenson testifies that the experts were both shocked and elated when they saw the self-portrait.
"This is a significant discovery because it contributes more knowledge to what we already know about Van Gogh's life," she told the BBC.
The Dutch artist is known for often reusing his canvases by turning them over and painting on the other side to save money.
The experts believe that it may be possible to obtain the hidden painting, but the process of removing glue and cardboard will require careful work and it is being investigated whether this can be done without damaging the front of the painting.