The company was awarded the contract to manage LFB's vehicle fleet by the London Fire and Emergency Planning Authority (LFEPA).
There will be a 10 day standstill period before the final contract award. Babcock said the contract is expected to become operational on 13 November 2014.
The company will be managing a fleet of 500 vehicles and 50,000 pieces of specialist equipment across Greater London.
Babcock will be investing in operational premises in Ruislip and Greenwich.
Peter Rogers, chief executive of Babcock, commented:
We look forward to working in partnership with the London Fire Brigade, supporting its delivery of vital services to make London a safer city and sustaining its status as a world-class fire and rescue service