UPM Tilhill will tackle soft and hard landscape at Howard Park and Gardens, created more than 100 years ago as a central part of the pioneering urban experiment.
Due to be completed next autumn, the work will preserve the historic importance of the site and use the new design to try to broaden the use of the park.
Commercial director Peter Middleton said: "We will work with the community, including schools and businesses, to deliver a leading contemporary facility."
Work will include refurbishing a paddling pool, creating improved play areas and building new routes. A reproduction statue of Sappho will also be installed, to replace the original stolen several years ago.
Funding has come largely from the Parks for People programme, run by the Heritage Lottery and Big Lottery Funds.