Developers Extreme said the Â£55m scheme for the Peak Parkway site would also provide an ice rink, other leisure facilities and housing.
The site has been confirmed as North East Lincolnshire Council's preferred location for the stadium.
One opposition councillor said the development is too large and in the wrong area.
Ian Barfield, Liberal Democrat councillor, said: "It just makes my heart sink.
"It is not a question of the town not needing economic development. It just does not need it on what should be an area of green space dividing the town."
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Extreme Leisure said a number of consultations will be held before any planning application is submitted.
Alistair Gosling, the company chairman, said: "This will provide inbound investment, local employment and better facilities for the locals and visitors of North East Lincolnshire."
About 320 full-time jobs could be created, excluding construction jobs, he added.
John Fenty, from Grimsby Town FC, said he was delighted with the proposals and was looking forward to the day "when the ground was broken".
The Labour leader of North East Lincolnshire Council said news of the deal was "very positive".
Councillor Ray Oxby added: "We have made it clear from the start that where there's the potential for public assets and resources to be involved, we must follow a strict and proper process to make sure we get the right result for the whole area."
Grimsby Town Football Club has signed a deal with a leisure provider to build a new 14,000-capacity stadium.