The last effort was rejected by Cumbria County Council in 2013, but local residents will be given more of a say this time, with the possibility of a referendum as a test of public support.
Building a Geological Disposal Facility (GDF) will create up to 2,000 jobs and bring in at least £8 billion to the UK economy, according to the Government.
The facility would be built at least 200 metres underground, made up of layers of steel, rock and clay to provide protection while some of the waste remains radioactive.
Waste is currently stored at 30 sites, including Sellafield in Cumbria, with estimates that a new facility would store 750,000 cubic metres of waste - enough to fill three quarters of Wembley stadium.
Energy Minister Richard Harrington said: "We owe it to future generations to take action now to find a suitable long-term site for the safe disposal of our radioactive waste, and it is right that local communities have a say.
"Planning consent will only be given to sites which have local support."
Communities willing to host a site will be given up to £1 million a year while the process continues, to be spent on areas such as skills and apprenticeships, but not for any shortfall in local authority spending.
The process to identify and and select a site requires detailed technical work estimated to take between 15 and 20 years, with the facility eventually running for at least 100 years.
The Government said the final decision on where to site a GDF will not be taken until there has been a test of local support demonstrating clear community backing.
Only two areas showed an interest last time - Shepway in Kent and Cumbria, where the council voted against preliminary work starting after concerns were raised about the local geology.
GDFs are currently being developed in Finland, Sweden, France and Canada, with experts arguing they are the only realistic way to dispose of higher activity nuclear waste for the long-term.
Consultations launched on Thursday will last for 12 weeks, with any Parliamentary process expected to take around 30 weeks.