The decision to build-on will cost £770m according to an independent consultants report, nearly 40% more than budgeted.
Now the council faces having to find £200m to bridge a huge funding gap just to get the first phase of the project, which is already three years behind schedule, finished.
City council officials have been given two months to produce detailed funding options to get the scheme up and running amid fears the council is facing a costly legal battle if it ends up pulling out of the project.
During a five-hour meeting, the full council considered a number of options, including scrapping the project.
On the table were choices to mothball the project and break the deal with contractor Bilfinger Berger at a cost of £750m.
The second option was to complete the original scheme in full but with no guarantee of the final bill. The third option was to press on regardless and complete the first phase of the disastrous project at a cost of £770m.
The consultant’s report said building to St Andrew’s looked the most favourable of the options available because it would earn £2m a year in profits when the tram became fully operational.
This option will also see Bilfinger Berger fullfil its pledge to fully fund the relaying of track in Princes Street, a section of the route beset with problems.
Eighty percent of the £545m budget has already been spent with huge sections still incomplete.
A long and bitter dispute between the tram company Tie and contractor Bilfinger Berger pushed the project over budget and behind schedule.
Conflicts have been blamed largely on utility companies failing to keep accurate records of underground pipes and a badly drafted original contract.
Mediation talks are understood to continuing after initial meetings between Tie and Bilfinger Berger were held in Glasgow in March.
Construction began in 2008 on the line which was due to run from Edinburgh airport through the city centre and eastwards to the old port of Newhaven.