The firm, which won one of the original main civils package for the site, will remove temporary stadiums, including basketball and water polo, and double the amount of parkland.
It will also have the task of reconfiguring Games-time bridges and underpasses under a new “Clear, Connect, Complete” programme of work designed to link nearby communities to the park.
“The appointment of Bam Nuttall will help set the foundations for a fantastic Olympic Park post the London 2012 Games,” Olympics minister Hugh Robertson said in a statement.
Around 500 jobs will be created in the process with at least 20% going to local residents in the host London boroughs and with training and apprenticeship opportunities on offer.
The project will be funded from the £292m budget set aside from the £9.3bn Olympic purse. The park will reopen in phases from July 2013.
Bam faces a tight programme, which is as challenging as preparing for the Games themselves.
The Olympic Park Legacy Company is keen that the Queen Elizabeth Olympic Park is opened as soon as possible and has set Bam the task of completing the north section by the summer of 2013 and the southern part by spring 2014.
Mace is overseeing the work as project manager with Bam, operating under a £49m contract for the north of the park and £27m price for the south.
The OPLC is also preparing to invite contractors to prequalify to bid for the £95m partial dismantling and rebuild of the Olympic stadium.
Removal of Athletes Training Centre at Eton Manor (temporary venue)
Removal of Basketball Arena (temporary venue)
Removal of Water Polo (temporary venue)
Removal of warm-up track (temporary venue)
Removal of Games-time security areas and spectator stands.
Around 9.5 km of the Games-time road network
Connect surrounding communities to the heart of the Park with new footways and cycle paths
Reconfiguration of 30 Games-time bridges and underpasses to improve public access.
Doubling of the amount of parkland to 102 hectares including the planting of a further 2,000 trees, ten hectares of meadow, new lawns and two large allotment sites.
Conversion of the Press Centre and Broadcast Centre site by removing the catering village and gantry to prepare for incoming tenant, and adding of photovoltaic panels and cladding to the car park
Create the Lee Valley VeloPark, including the addition of a 1.6 km outdoor cycle circuit, a 6.5 km mountain bike trail, the regarding of the BMX circuit and internal work to the Velodrome
Create the Lee Valley Tennis Centre and Lee Valley Hockey Centre on the Eton Manor site for Hockey and Tennis
Internal fit-out of the Multi-Use Arena for public use
Reinstate 12 football pitches at East Marsh