Eric Pickles, the secretary of state for communities and local government, has decided not to call in the scheme after North Somerset Council granted full planning at the end of July.
Sir Robert McAlpine is aboard as main contractor for the huge project and will start construction at the end of the year.
The Leisuredome will be built on a 12.7-acre site at Locking Parklands, a former RAF site that is undergoing a £400m housing redevelopment into a sustainable community by developer St Modwen.
It will boast the longest ski slope in the UK at 210m, and an indoor climbing centre with a 40m high climbing wall, claimed as the world’s tallest.
The centre will also house an indoor surfing centre and sky-diving facility, children’s centre, BMX skateboard park, and gymnasium.
Clive Hamilton-Davies, director, Leisuredome (UK): “This is significant milestone for the Leisuredome team and we are absolutely delighted that permission has been granted for the development to now proceed.
“We hope that the Leisuredome will provide tremendous benefits to residents, local businesses and the wider community and look forward to working in partnership with the local community to make Leisuredome a great success.”