Council chiefs and trams firm TIE announced they had successfully concluded negotiations with German and Spanish contractors, covering vehicles, track and other infrastructure.
And the price they agreed is 512 million – 14m more than originally expected, and 1m more than reported in the Evening News on Monday.
The first tracks will be laid by September this year and the first tram is set to run in Edinburgh in July 2011.
Protracted contract negotiations and record low exchange rates against the euro have been blamed for the price rises.
In a statement, the council and TIE said the final contract negotiations had been conducted in "difficult and uncertain international economic conditions", combined with "an extremely heated UK construction sector".
The statement stressed the price remained within the 545m funding figure set for the project.
The tram tracks and overhead wires will be supplied by a consortium, Bilfinger Berger Siemens (BBS), whose members have been involved in the construction of over 30 urban transport schemes around the world.
The tram manufacturer, CAF, is best known in the UK as the company that provided the first train fleet for the Heathrow Express in a consortium with Siemens. It has recently supplied the trams to Seville's new tram system and has put into service a fleet of trains for Northern Ireland Railways.
TIE chairman Willie Gallagher said: "I'm pleased that these negotiations have now reached a successful conclusion.
"These pressures on costs are not isolated to the tram project. The fact is that every major construction project in Scotland and in the UK is and will be impacted by these exact same factors. We have sought to successfully deal with them now.
"From the start of the procurement process my team set out to drive a fair and hard bargain."
He said TIE had brought together an international project team with experience from all around the world.
And he added: "We look forward to building the Edinburgh tram project on time and on budget."
City council leader Cllr Jenny Dawe added: "I am delighted the intricate and tough negotiation period has reached a satisfactory conclusion. This has not been easy, particularly in the prevailing global economic situation, but I am confident we have a fair deal.
"We are now well on our way to delivering an excellent tram project for Edinburgh that will connect vital growth areas in the city and provide a first class modern, attractive and additional means of public transport."