The archive will convert more than 2,000 issues, or a quarter of a million pages, from print to a searchable, digital format accessible for free by the public.
The project is currently in development with a set of interested parties, including the Institute of Historical Research, and will be completed in time for the grand opening of the Museum's new Galleries of Modern London next year.
The archive aims to be an important chronicle of the evolution of London news, arts and culture, from the perspective of Time Out. It hopes to provide an insight and record of the events and institutions that have shaped the lives of Londoners.
Tony Elliott, chairman of Time Out Group, said he is "enormously proud" with the partnership. He added: "The archive will preserve 41 years of London life for future generations and will continue to develop as a repository for cultural material that will help bring the rich fabric of London's story to life."
The official launch is taking place tonight (1 June) at a reception at the Museum of London.