The extra money allocated for 2022-23 will bring the total provided by the Scottish Government to more than £12.5 million.
It is now more than three-and-a-half years since the inquiry’s public hearings finished, and seven years since the inquiry under Lord Hardie was announced.
The inquiry’s objectives included learning lessons from the tram line construction fiasco in which the project was finished years late and hundreds of millions of pounds over budget.
Construction work to extend the Edinburgh Airport-York Place route to Newhaven is well underway, with trams due to start running in spring 2023.
However, further lines in the capital are planned under the Scottish Government agency Transport Scotland’s latest strategic transport projects review.
The inquiry said it was making “good progress”, but the Scottish Conservatives said the situation was highly unsatisfactory.
Lothians MSP Sue Webber said: “There seems to be no end in sight for the Edinburgh tram inquiry.
“Once a beleaguered project is now a much beleaguered public inquiry that has managed to siphon off another £500,000 of public money.
“SNP ministers must question why no report has been delivered when closing submissions concluded in 2018. and costs have spiralled.
“With Parliament three times declining urgent questions from the Scottish Conservatives, Edinburgh residents deserve answers into what went wrong with the building of the trams."
A Transport Scotland spokesperson said: "We have agreed to continue to fund the costs of the Edinburgh tram inquiry until it is completed.
"The amount spent on the inquiry to date is just over £12m.
"Final costs will be published when they become available.
“As a statutory inquiry, it is independent of Scottish Government.”
City of Edinburgh Council leader Adam McVey said: “We’ve supported the tram inquiry throughout and look forward to its conclusions.
"The team delivering the Trams to Newhaven extension have done a brilliant job in the most difficult of circumstances and have managed to keep the project within budget.
"In the context of Covid, this is a remarkable achievement.
"The team have already taken lessons on board from the previous project in order to deliver this so successfully to date, but any additional findings that the inquiry eventually publish will also be looked at too.
“I’m sure the inquiry will also help inform other authorities looking to invest in similar major transport infrastructure projects, as councils invest to improve sustainable transport choices and tackle climate change.”
A spokesperson from the Edinburgh Tram Inquiry said: “Lord Hardie’s remit is to conduct a robust inquiry and he has made it clear 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.
"The inquiry’s evidential database contains over 3m documents that have to be carefully considered, which is an extensive but vital task.
“We continue to make good progress towards producing the final report and recommendations, which will be published as soon as practicable.
“The Inquiries Act 2005 obliges the chair to consider cost at all times since it is funded from the public purse.
"Throughout the process all efforts have been made to ensure the Inquiry delivers best value.”