The IPPR North document says key Common Agricultural Policy funding and powers should "leapfrog" from the EU to devolved areas post-Brexit.
This should be done within the context of a national industrial strategy framework, it suggests.
Called Forgotten opportunities: The dynamic role of the rural economy in post-Brexit Britain, the report says policy should be better linked to local priorities.
This report presents a place-based approach to rural policy that addresses local, national and global issues effectively, and recommends the introduction of 'rural devolution deals'.
Local and combined authorities would be given the power to improve food production, the environment, industrial strategy and capital spending to support infrastructure and development.
Britain's rural areas represent a forgotten opportunity, says the document. Their economic contribution – 16.6% of GVA – derives from diverse activities, it says.
Traditional rural sectors such as agriculture and tourism operate alongside a growing presence of agri-tech, energy generation, and manufacturing.
The latter accounts for the same proportion of the rural and the urban economy.
But rural challenges arise from remoteness, lack of investment, mistaken or outdated assumptions about rurality, and the application of policies designed primarily for urban areas.
Different elements of the rural economy are closely intertwined, relationships to urban neighbours are important, and rural places themselves are highly diverse, says the document.
Policy for the rural economy in the 21st century needs to recognise this integration of issues and the importance of place, it argues.
Brexit brings the chance to take an innovative and transformative approach, updating agricultural policy and addressing new opportunities and challenges, says the report.
A place-based approach to rural policy offers the best mechanism to deliver rural policy which both addresses national and global issues and responds effectively to local need and diversity.
The study recommends 'rural devolution deals' in which central government sets 'minimum obligations' which local areas with a substantial rural component must meet.
The proposal would see local authorities working with local enterprise partnerships to demonstrate how they will use devolved budgets to meet their obligations and add value.