Balfour is already working on the £41m stadium roof contract which it won last summer.
Original stadium builder Sir Robert McAlpine was widely expected to land the main conversion deal.
But Balfour has triumphed in a hard-fought race with McAlpine, Buckingham, ISG and Shepherd.
The new stadium will be home to West Ham United from 2016 who are desperately trying to cling-on to their place in the Premier League as they fight a relegation battle.
The new venue will also host five matches during the Rugby World Cup 2015 and become the new national competition stadium for athletics in the UK.
A new community athletics track will also be provided next to the main Stadium.
Sustainable construction methods will include features of the existing facility being recycled and incorporated into the new stadium and the re-use of crushed demolition material, existing balustrades and sanitary ware.
Works starts on site early this year and is due for completion in the spring of 2016.
At construction peak the project will employ up to 400 people.
Once reconfigured the stadium’s cable net roof – 84 metres wide at its deepest point – will be the largest cantilevered roof in the world covering every stadium seat, improving acoustics and spectator experience.
Balfour Beatty Chief Executive, Andrew McNaughton said: “We are delighted to be continuing our activity at the Queen Elizabeth Olympic Park supporting the legacy commitment made as part of the London 2012 Olympic and Paralympic Games.
“During construction, our firm commitment to the use of local labour and the creation of apprenticeships will continue to benefit the local community and the wider industry and, upon completion, the stadium will provide a first-class sporting and cultural facility for many generations to come.
“Balfour Beatty is proud to be associated with this project.”
West Ham Vice Chairman Karren Brady said: “I, along with my team, will be working closely with the LLDC and Balfour Beatty every step of the way to ensure that the conversion delivers a Stadium that West Ham fans can be proud of and that guarantees them an unrivalled experience on a matchday.”