First Minister Alex Salmond announced that a judge-led inquiry would be held to determine how the infrastructure scheme became mired in delays and cost overruns, just days after the trams finally began running through the city.
However, key witnesses behind the fiasco could refuse to give evidence as the inquiry will be non-statutory, meaning the judge cannot compel individuals to appear.
Although Edinburgh City Council has agreed to co-operate fully with the inquiry, the arrangement opens the doors for other key witnesses, such as former TIE bosses Willie Gallagher and David Mackay or contractors Bilfinger Berger/Siemens, to refuse to give evidence.
Campaigners had been calling for a full public inquiry under the terms of the UK's Inquiries Act (2005), but the Scottish Government said a non-statutory equivalent would be a quicker and more efficient route to uncovering what went wrong because it offered the judge greater flexibility.
It comes after criticism over lengthy statutory public inquiries, such as the probe into the Vale of Leven Clostridium difficile outbreak, which began hearing evidence in 2010 and has yet to report its findings.
Speaking at First Minister's Questions yesterday, Mr Salmond said it was vital to understand what went wrong in order to prevent similar mistakes in future.
He said: "I'm sure everyone in Edinburgh and indeed all over Scotland will be delighted to see that the Edinburgh trams are fully operational and carrying passengers.
"We cannot, however, lose sight of the considerable public concern about the project, the disruption it caused to households and businesses in Edinburgh.
"I have therefore recommended to the Cabinet and it has been decided to establish a judge-led public inquiry to inquire into the Edinburgh trams project, to establish why the project incurred significant overruns in terms of cost and timing, requiring in particular a considerable reduction in the original scope.
"It is particularly important if any projects like it are being considered in the future that lessons are learned."
The scope, timetable and details of the inquiry, including which High Court judge will chair it, have yet to be confirmed but further details are expected before the summer recess.
Daniel Donaldson, an Edinburgh sdolicitor who has spearheaded the campaign for a public inquiry, said evidence should be heard from those affected by the chaos as well as those behind the project.
He said: "The terms of reference must afford those affected by the Edinburgh Trams fiasco the opportunity to have their voices heard.
"The terms must also allow a full forensic analysis of where the money was spent, whether the business case was actually viable, the qualifications or lack of experience of those put in charge, the contracts written, the forward planning that took place, the politics behind the project among many other important issues.
"Lessons will have to be learned from this project, and politicians and public officials will be held to account for their maladministration."
Trams began running in Edinburgh on May 31 this year, bringing to an end a saga which saw the cost to taxpayers balloon from £375 million to £779m at the same time as the route halved and the timescale doubled.
Scottish Labour's Shadow Minister for Transport, Mark Griffin MSP, said: "Given the massive cost to the taxpayer, far in excess of what it should have cost, the impact on residents and businesses in Edinburgh and the long-term ongoing financial cost to Edinburgh, this decision is right.
"Taxpayers, businesses and the people of Edinburgh need to understand what went wrong and how this can never happen again.
"This is not the first or only major public contract which has not run to time or budget. I hope that this inquiry provides the lessons we need to ensure that the way in which we contract, organise and deliver these projects in the future means that this never happens again."