The project, which forms part of a new masterplan in the Kent town, was drawn up by local practice CTM Architects.
The major element of the scheme's brief is that the new designs must not over-run the £15 million budget set by Kent County Council.
Council leaders said the masterplan and the new site for the gallery would allow the client body to keep much stricter control over the purse strings on the project.
In February the council dropped Snøhetta and Spence's proposals, claiming that the budget had spiralled out of control to £50 million.
Kent County Council (KCC) leader Paul Carter said he was 'honouring a promise made eight weeks ago when the spiralling cost of the original Turner Contemporary site led to the rethink'.
'I think it is vital that people in [the local borough of] Thanet hear openly and at first-hand what we are trying to do. The gallery project is absolutely secure, but there is far more potential for unlocking regeneration.
'The Winter Gardens [part of the masterplan area] are an architectural jewel and deserve a renaissance. We have a superb and interesting coastline backed by the old town. I believe the potential is enormous,' Carter added.
KCC will now look to select an architect to draw up detailed designs for the new Turner Contemporary, which it envisages opening in 2009.