The agreement will see £150m of conversion work carried-out to transform the stadium into a 54,000-seater venue for the Premier League club.
The Hammers will start playing in Stratford from the 2016/17 season.
Conversion works will include a new roof, corporate areas, toilets, concessions and retractable seating.
The main shell-and-core contract is currently out to tender with original Team Stadium team led by Sir Robert McAlpine among the favourites.
A separate roofing and steelwork package was also put out to tender this week.
A funding deal has been struck for conversion works which will see West Ham contribute £15m.
Newham Council will invest £40m and the Government £25 million with the balance coming from the Legacy Corporation.
West Ham Vice Chairman Karren Brady said: “It was important to me that we struck a deal that would stand the test of time that represented the right deal for West Ham United and our loyal and patient supporters.
“The consultation we have promised them will now begin and we can’t wait to work with them to create a stunning new home that befits the pride, passion and tradition that the world associates with West Ham United.”
The Stadium will also become the new national centre for athletics.
UK Athletics has been given priority use of the venue from the third weekend in June to the end of July every year, under a 50 year agreement, while the Stadium will host the IAAF World Athletics Championships and IPC Athletics World Championships.
The Legacy Corporation is also looking to accommodate matches from the 2015 Rugby World Cup during the transformation work.