Work to create an Eden Project on the East Dock Street site of the city would include the conversion of the existing gasholder and demolition of other buildings on the site.
A separate application to create a pedestrian bridge that will span across East Dock Street and the east coast mainline railway will go before planners for approval later this year.
The £130m project will consist of three different venues which, Eden Project bosses say, would showcase wild landscapes, exhibits, art installations, performances, and storytelling.
Work is not expected to start for two or three years allowing time for full financing to be secured.
Blair Parkin, the Eden Project’s chief experience development officer, said: “We are delighted that Dundee City Council has granted us planning permission for Eden Project Dundee.
“This is a major milestone for the project and the culmination of years of hard work by the Eden Project team, our partners in Dundee and the community who have engaged with us so generously.
“We will allow ourselves a moment of celebration but we are well aware there is still lots to do to make Eden Project Dundee a reality.
“We will now concentrate on working with all our partners, progressing the design, securing investment and continuing to deliver our community programmes in the city.”
The Eden Project is working in partnership with Dundee City Council, The Northwood Charitable Trust and the University of Dundee.
The project team includes architect Feilden Clegg, structural engineer Expedition Engineering, M&e consultant Atelier Ten and cost consultant Aecom.