The scheme will see hydrogen generated from water using the solar array and wind turbine already in operation at Featherstone House farm, on Mickledale Lane.
Advocates say the new approach to producing fuel from sustainable and renewable sources can help the UK shift to carbon neutral energy.
Tim Shuldham, a senior partner at property consultants Fisher German and director of landowner CA Strawson Farming Ltd, said: “Tony Strawson and his family have been innovators in farming and this is an obvious direction for them to move in.
"This scheme has the potential to deliver stored energy to end users which could, for instance, be hydrogen-powered buses in a city centre or farm machinery.”
The development consists of a 1.25 megawatt electrolyser inside a building, based within a secure compound.
The electrolyser will produce hydrogen which, once turned back into electricity through a fuel cell, only emits water vapour and air.
The hydrogen could be sold on off-site or used to power vehicles on the farm, helping the business meet its own carbon neutral objectives.
While there are no specific planning policies for hydrogen energy schemes as yet, the council expressed full support and took less than nine weeks to grant approval.
Sarah DeRenzy-Tomson, who led the planning process at Fisher German, said: “We are pleased to have secured consent on behalf of the landowners, who are particularly keen to promote sustainable energy and embrace innovative technologies.
"This is a new area of technology and only a handful of planning applications have been approved for schemes of this nature, but we expect them to become increasingly popular in the years ahead.”
She added: “The development appears industrial in character, which is not normally appropriate in a countryside setting, but the local authority understood the merits of locating it adjacent to the electricity generators.
"The council also recognised the environmental benefits of the scheme, as the Government looks to reduce greenhouse gas emissions by at least 80 per cent by 2050, compared to 1990 levels.”