The firm will replace current franchisee Serco which has operated the service since 1997.
Keolis already runs a number of UK rail services through Govia which it co-owns with the Go-Ahead Group and which recently won a seven year franchise to operate Thameslink.
TfL says the new operator will be expected to deliver improvements to the service while meeting growing demand.
The £700m contract will start on December 7th and run until April 2021. TfL has an option to extend the deal for a further two years.
Mike Brown, TfL’s Managing Director of London Underground and Rail, said: “The DLR is a rail network that continues to support regeneration across a huge area of London and the economic growth of the city as a whole.
“The decision to appoint Keolis Amey Docklands was reached after a thorough and competitive procurement process, which will ensure the DLR continues to deliver an ever-improving high quality, value for money service for Londoners well into the future.”