The development, part of a 10.5m investment programme, will replace existing "tired" facilities.
Northumberland National Park (NNP), which has issued the £300k architectural tender, said the design should "sympathetically reflect the landscape" and "maximise positive environmental impacts".
Priority would be given to proposals that provided training for design and construction skills.
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NNP said the visitor centre would be sited at Once Brewed, where a youth hostel has been present for more than 50 years and would provide a "hub" for Hadrian’s Wall’s million visitors a year.
The authority hoped the centre would attract more domestic and international tourists to the lowest-visited National Park in the UK.
An NNP statement said: "Any new development within a National Park and a World Heritage Site will rightly come under close scrutiny. The draft architectural and interpretive design brief emphasise the requirement to exemplify the special qualities and values of Northumberland National Park, and the designs will involve comprehensive public and partner consultation."
Expressions of interest must be received no later than July 19, via www.mytenders.org, and the successful tender will be submitted for planning permission in late April 2013.
(NE)
