Showcasing the covers from the last nine decades, the exhibition includes covers from the 1966 World Cup, the outbreak of war in 1939 and the London 2012 Olympic games.
Queen Elizabeth II's coronation in 1953 was also commemorated in a full-colour front page.
The first issue, published in 1923, positions the magazine as "the official organ of the BBC" and was created in response to director general John Reith's rejection of calls from newspapers to charge the BBC to print its listings.
Celebrities featured on the front pages across the 90 years include Eric Morecambe and Ernie Wise, Mick Jagger and, in the most recent issue, Steve Coogan as Alan Partridge.