The show, at the Museum of London, focuses on the character of the great detective and the city where most of his adventures were set.
Alex Werner, head of history collections at the museum in central London, said: "You can't have Sherlock Holmes without Watson and you can't have the two of them without London. For me London is the third character, the essential element in the stories."
Exhibits include an original manuscript of one of the stories written by Arthur Conan Doyle, the coat and a dressing gown worn by Cumberbatch in the hit TV version and a portrait of the author by Sidney Paget who illustrated the original stories.
Mr Werner said Conan Doyle's depiction of London with Holmes and Watson chasing through foggy streets was an accurate picture of the capital at the turn of the century.
He said: "We like to think we are further away from that world than we are. It was a time of huge information overload, there were lots of newspapers coming out with so many stories and adverts and Sherlock Holmes could cut through all that and see things other people couldn't."