Both sides have been in intense negotiations since a formal mediation process started in March after major construction work stopped two years ago following a dispute over who should pay for additional costs.
Bilfinger Berger, Siemens and CAF will now restart remedial work on Princes Street this month while the timetable for other works will be announced shortly.
Council Leader Cllr Jenny Dawe said: “This is an important milestone in restoring our vision for a clean, green and efficient transport system in Scotland’s capital.
“It is essential for everyone who lives or works in Edinburgh that the project gets going now as soon as possible.
“I am pleased with the spirit of cooperation shown by all parties and grateful for the hard work that has gone into taking us forward.”
Council Chief Executive Sue Bruce said: “An incredible amount of effort has gone into addressing all the issues that have made this such a challenging project.
“However, the real work begins now on getting the line finished and the trams running.
“As with any major construction project I’m sure we will have hurdles to overcome, but our new governance and operational arrangements are aimed at dealing with those as efficiently as possible.”
The revised timescale for completing the line from Edinburgh Airport to York Place is summer 2014 and Turner and Townsend will act as the Council’s project management consultants.