The site is due to host five matches during the Rugby World Cup in 2015 and will be the permanent home of West Ham Football Club from 2016.
Last summer Balfour was awarded the contract to convert the stadium roof and will now lead the remainder of the transformation works after winning the contract from E20 Stadium Partnership, which is a joint venture between the London Legacy Development Corporation and Newham Council.
During construction Balfour expects to employ up to 400 people and will work with Workplace, Newham Council's employment service, to hire local people where possible. Balfour is also committed to providing apprenticeships amounting to 7% of the total workforce.
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.
Balfour chief executive Andrew McNaughton said the stadium will provide a first-class sporting and cultural facility for many generations to come. He added: "Balfour Beatty is proud to be associated with this project."
The site will also be a new national competition stadium for athletics in the UK, hosting regional and national age group championships, as well as elite international events including the 2017 IAAF World Championships.
Balfour delivered a number of projects for the London Games, including the Aquatics Centre and a £150 million package of roads and bridges.