Stewart Park, which opened to the public in 1928, is to undergo a restoration project that includes de-silting a lake, tree and shrub planting and hard landscaping.
The work on the 47ha park is part of a revamp being funded in part by a grant through the Heritage Lottery Fund and Big Lottery Fund Parks for People programme.
The park was formerly the estate of a Victorian mansion and contained the cottage, now demolished, in which Cook was born.
The park masterplan was created by Southern Green landscape architects and the firm is to run the contract once a landscaper is appointed.
Middlesbrough Borough Council principal landscape architect Peter Small told HW the successful firm would need to get around the challenge of "sequencing issues" as the park would remain open to the public throughout the work.
Work is expected to start in November and take around 14 months to complete. The deadline is 13 May. Call Stephen Snaith on 01642 729178.