Campaigners delayed the signing of a contract between the council and Balfour Beatty after launching legal action claiming the council had no right to build the new Portobello High School on common land in the city.
They lost their case but have lodged an appeal, which is due to be heard on 24 May.
But yesterday councillors approved a report to allow work to start immediately after the legal action has finished and sign a contract with Balfour Beatty.
Plans for the new school were first approved by the council in 2008, which will feature a 25m swimming pool and sports pitches for community use.