The developer is set to transfer the broadcaster's staff to the proposed base in Hanover Street as part of a regeneration programme.
The move is necessary because the existing BBC building is part of the Paradise Street area of the city, which Grosvenor is to redevelop.
The buildings were the subject of a compulsory purchase order application, which has been reviewed by the Office of the Deputy Prime Minister after tenants raised objections to the £750m redevelopment proposals.
This inquiry has just decided in favour of the developer's proposals and the CPO.
A spokesperson for the BBC said that the Hanover Street building, which will be designed by the Glasgow practice Page and Park, would fulfil the same role as the existing premises.
She said: "Part of the deal with Grosvenor Estates is to give us a like-for-like building in Hanover Street, to make way for the Paradise Street development."
The BBC spokesperson added that the corporation was looking to raise its profile outside London.
She said: "The BBC has strong production bases throughout the UK. However, to serve our audiences better we are exploring opportunities to increase the BBC's regional presence."
One way in which this could be done is to move some of the BBC offices out of London – one of the ideas being considered as part of the government's BBC Charter review.
Grosvenor Estates' 17 ha Paradise Street project is scheduled for completion by 2008, when Liverpool will be European City of Culture.
It links directly to the business district and the waterfront.
In December 2002, Liverpool council and Grosvenor Estates signed a development agreement to carry the project forward, and planning approval has been granted.
The Hanover Street premises is scheduled to open in summer 2006.