Scottish Government figures last month revealed the cost of the inquiry, chaired by former Lord Advocate Lord Hardie, had already reached £6.5 million – more than six times the original estimate of £1m.
And politicians warned the inquiry could end up being more expensive than the £10.2m Chilcot Inquiry into Iraq.
Lothian Tory MSP Miles Briggs tabled a question asking when the inquiry would complete its work.
In a written answer, Mr Yousaf said: “Lord Hardie and his team are determined to conduct a thorough and wide-ranging investigation into the reasons behind the Edinburgh Tram Project delays and cost escalations and to deliver a report and recommendations to ensure lessons are learned for future major infrastructure projects.
“It will take as long as is necessary to get the answers the public wants in relation to the issues surrounding the Edinburgh Trams Project.”
He claimed “good progress” had been made including identifying, retrieving and reviewing more than six million documents. The tram project was originally supposed to cost £375 million for 15 miles of track and be completed by 2011, but a truncated nine-mile route from the airport to York Place was opened in 2014 at a cost of £776m, with interest charges expected to push the final bill to around £1 billion.
When the then First Minister Alex Salmond appointed Lord Hardie to head the tram inquiry in June 2014, he promised it would be “swift and thorough”.
Mr Briggs said: “Just like the tram itself, the tram inquiry is overdue, many times over budget and is costing taxpayers far more than they ever expected – and we still don’t know when it’s going to reach its conclusions.
“It is quite clear the SNP Government has lost control of an inquiry it set up and has absolutely no idea when it will report. The then First Minister Alex Salmond said he looked forward to a ‘swift’ inquiry and the Scottish Government assured us it would be ‘carried out quickly, efficiently and cost effectively’.
“Now we have the Transport Minister telling us the inquiry will take as long as is necessary so the previous assurances from the Scottish Government can be seen to be totally worthless.
“Edinburgh residents are concerned and annoyed at both the length of time the inquiry is taking and the millions of pounds of money that it has incurred so far.
“The Transport Minister should be responding to public concern and not just passively saying that it will take as long as is necessary with no indication of when this will be.”