The London practice will draw up plans for a series of visitor facilities, new pathways, an aerial walkway and a series of new bridges.
The client, an organisation called the Heart of the National Forest Foundation, said it picked Cullinan because of his pedigree in innovative timber construction, exemplified by the Stirling-shortlisted Gridshell at the Weald and Downland Museum in Sussex.
Cullinan's work will form the key part of the Heart of the National Forest Foundation's bid for £25 million from the Big Lottery Fund for the 400ha project.
Foundation chairman Stephen Woolfe said he was delighted to have taken on Cullinan, whom it has been agreed will lead the design team himself.
'Ted Cullinan, and the architectural practice he founded, are famous across the UK and overseas for designing spectacular buildings that are environmentally friendly and that combine great beauty with sustainability.
'There could really be no better architects than these to produce the first designs for our Lottery bid,' he added.