Scheduled to open in 2011, EARL will link air passengers with 62 stations across the Scottish rail network.
The scheme was voted through by 86 votes to 29 with three abstentions at a final stage debate at Holyrood on Wednesday. SNP politicians believe the cost could run to £1 billion, and the Green Party was also sceptical that the new rail line was value for money.
Aedas' project manager John Kinsley said: 'There are strong aspirations that the design for this transport hub will set a precedent for similar facilities in the future. We have worked hard - to develop a gateway piece of sustainable architecture. Our plans will evolve as we continue to consult with the client team and stakeholders.'
The project is backed by Transport Scotland, the national transport agency for Scotland, and is developed in consultation with the City of Edinburgh Council, the British Airport Authority and Network Rail.