The firm beat rivals Carillion, Kier and Skanska to take the job which has been in procurement for two years and was originally costed at £130m.
The main barracks redevelopment will help accommodate two new signal regiments returning from Germany.
Lend Lease will design and build single living accommodation, regimental headquarters, mess and catering facilities, technical workshops and medical and dental centre facilities.
It will involve the construction of 25 new buildings and the refurbishment of eight existing buildings.
A parallel project will provide some 360 military houses on MOD-owned land next to the barracks for service families stationed in Stafford.
Seddon Construction, Lend Lease Construction, Lovell Partnerships, Mansell and Bouygues-owned Thomas Vale Construction are drawing up tenders for this element of the project.
Work at Beacon Barracks is expected to start immediately and the barracks will remain home to 22 Signal Regiment and the Tactical Supply Wing while it is taking place. The MOD is currently working with local authorities and service providers in Stafford to prepare for the arrival of the two regiments.
Stuart Gallacher DIO Project Manager said: “DIO’s priority is to support our Armed Forces by providing the best possible facilities for them to live, work and train.
“Today’s contract award marks a significant milestone in this important programme which will not only bring a boost to the local economy by the relocation of two regiments but will also help provide value for money for the taxpayer.”