Mr William Nicholson was awarded the medal for graphic design at the games in the Netherlands.
At the time the Olympics also awarded medals for architecture, literature, music, painting, and sculpture, a practice that continued until 1952.
Mr Nicholson’s medal for his sports picture almanac, Un Almanach de douze Sports, forms the centrepiece of the exhibition, along with personal items, including his dressing gown, waistcoat and bow tie, photographs and sketches on loan from his grandson, Mr Desmond Banks, of London.
Museum curator Mrs Patty Temple said Mr Nicholson only found out at the last minute that his work had been submitted by his publisher Heinemann and had won a medal.
She said: “He nearly didn’t make it to the award ceremony.
“He had to run out of his house and get on the first plane to Amsterdam, which was the first time he had ever been on a plane, and he just made it in time.”
Mrs Temple said the exhibition aimed to give visitors an insight into what Mr Nicholson was like as a man as well as an artist.
She said: “We wanted to select some of the more personal items but there really was so much to choose from we could have easily filled the whole room.”
Mrs Temple said as well as linking with the Olympics the exhibition also had a strong civic connection as both Mr Nicholson’s father and grandfather were mayors of Newark.
Mrs Jill Campbell, a member of the Friends of Newark Town Hall Museum, helped to put the exhibition together.
She said Mr Nicholson had many influential friends, including Winston Churchill, who he tutored in art during the 1930s.
Mrs Temple said she was hoping Mr Banks would be able to visit the exhibition along with his mother, Lisa, Mr Nicholson’s daughter, who is 91.
The exhibition continues until Saturday, June 30.