Former transport minister Stephen Byers approved the scheme last November on the condition that two rivers running across the proposed site were diverted.
The Government Office for London this week wrote to BAA confirming that a proposed double channel reroute had met with the secretary of state's approval.
BAA's original plan was to provide a single channel around the site enabling both rivers to run around the airport. However, it was later decided that a double channel for the rivers would be more suitable.
A BAA spokesperson confirmed that the Government Office for London had given permission to reroute the two rivers. He said: "This decision was expected, as the London Borough of Hillingdon had approved the plans. However, we have this week received the final piece in the planning jigsaw."
We have received the final piece in the planning jigsaw
BAA said it expects the terminal to be open by 2007 – 14 years after it originally applied for permission.
A four-year, £80m public inquiry into the scheme concluded on 17 May 1999 and was the longest of its kind in the UK. The official inquiry report landed on ministers' desks in December 2000 and last November the scheme was approved, pending the conditions that have now been met.
A decision is due before September when a preferred bidder from a shortlist of Amec and a Laing/Fitzpatrick/Stenoak joint venture will be selected.