The team has beaten off bids from Mowlem and HBG for what is one of the largest construction projects in the UK.
Bovis Lend Lease/Multiplex now has five months to negotiate the contract. Work is expected to start on site in the autumn.
The award of the contract also means that Australian arch-rivals Lend Lease and Multiplex will be working together for the first time. Bovis had teamed up with Multiplex to bid for Wembley before it was bought by Lend Lease.
Wembley chief executive Bob Stubbs said: “This is another of the milestones on the redevelopment that we have hit on target.”
Bovis Lend Lease chairman Sir Frank Lampl added: “The combined experience of Bovis in Atlanta and Multiplex in Sydney demonstrates the level of expertise we shall bring to focus on making Wembley the success that it deserves to be.”