The new museum will be based in the cells and offices of Bow Street Police Station
Bow Street Police Station and Magistrates' Court opened in Covent Garden in 1881, but it was closed a number of years ago.
From early 2021, the building's ground floor cells and offices are to open up as the Bow Street Police Museum, telling the history of local policing.
Manager Vicki Pipe said they "cannot wait to welcome our first visitors".
Bow Street was home to London's first professional police force, the Bow Street Runners, which was founded in 1749.
The Met Police later opened a police station in Bow Street and a magistrates' court was set up next door.
Numerous famous faces came up before its judges while it was operating, including Oscar Wilde, suffragettes Sylvia and Christabel Pankhurst, and the Kray Twins.
The police station eventually shut in 1992, while the magistrates' court closed in 2006.
The new museum will examine the work of the Bow Street Runners, while also sharing the stories of the people who worked in the building and those who faced its judges.
Exhibits will include the original dock from Court no. 2, equipment used by the Bow Street Runners, and personal equipment from former officers including beat books and truncheons.
Visitors will also be able to spend time in a cell called "the tank", which was often the destination for those arrested for drunken behaviour in Covent Garden.
Curator Jen Kavanagh said she hoped guests would get "a real sense of the history of Bow Street and the people who have passed through those doors".
"We have worked especially closely with officers who served at Bow Street and, as a result, the museum is rich with recollections of life at a unique place in a special part of town," she added.
Those behind the museum hope to open it early next year, subject to Covid regulations in the capital.
London is currently in tier three meaning entertainment venues like museums must remain closed.
The government was set to protect man from criminals, and the Constitution was written to protect man from the government.