The firm was selected following interviews with north-east Somerset council and the South West Regional Development Agency last month.
Grosvenor and the council are currently in talks over the agreement, expected to be signed by the end of April. At this point Grosvenor will be able to start acquiring land on the site, a process which will be complicated by the number of different landowners.
Local MP Don Foster said that, despite the latest development, the project still has a long way to go. He said: "I guess it's going to be three years before we see the cutting of any sods. The land has already been derelict for upwards of 25 years."
Foster would not confirm that Grosvenor was the chosen bidder. There is a confidentiality agreement between the developer and the council.
Once a contract is signed, Grosvenor will have a variety of initial responsibilities. These will include acquiring land, demolition work, remediation and improvement of local transport infrastructure.
Originally 18 developers were invited to pitch for the project, although only six expressed an interest.
Foster is today due to chair a debate on the future of the site, which is expected to be attended by representatives of Landscape Estates and the Council for the Protection for Rural England. Both groups have independently drawn up alternative plans for the development.