An agreement reached with the Scottish Government will result in City of Edinburgh Council picking up the cost of extending the use of free bus passes to journeys on the eight-mile tram line when it is completed next summer.
The National Concessionary Travel Scheme offers unlimited free bus journeys to disabled passengers and those over 60.
However, there have been years of negotiations over whether to extend this to tram travel once the troubled £1 billion scheme is completed.
The tram deal was welcomed by the SNP and Labour, though the Tories warned it would lead to funds being diverted from key council services.
The council would not say how much the move would cost, saying only it would now "explore options for council funding".
Transport Convener Lesley Hinds indicated "joint funding" between the council and the Scottish Government could be secured once more details were known about how the scheme would operate.
This was flatly denied by Transport Scotland, the Government agency which has provided £500m funding for the tram project, whose spokesman said there was an "unequivocal" decision the council would pay for extending the free scheme.
Transport Minister Keith Brown said: "This is good news for local residents in Edinburgh and the aim is that this scheme will help promote integration between the tram and local bus services in the city.
"The Scottish Government is providing £500m in financial support for the construction of the Edinburgh trams project.
"Local authorities have also received a fair three-year settlement from national Government for 2012-15 and as part of that, the council is receiving an extra £68m over the three years to disburse as it sees fit."
The cost of the trams scheme has nearly doubled, including interest payments for borrowing, from its initial budget of £545m as the length of the route was slashed. It is not clear how much it will cost for the travel scheme to be extended, in part because fares are yet to be agreed.
However, based on Lothian Buses' flat fare of £1.40 for an adult single and using council forecasts of passenger numbers released to The Herald, the cost would be £1.5m a year initially, rising gradually to nearly £3m a year after 20 years.
Using a higher fare, such as the £3.50 charged on Lothian Buses' Airlink service, would result in the costs more than doubling.
Alex Johnstone MSP, the Conservative's transport spokesman, said it was "another classic example of mismanagement of the trams scheme".
He added: "Taxpayers in Edinburgh have suffered enough as a result of this project. It's not fair they now pay for the journeys of those aged 60 and over, many of whom can well afford it.
"Lothian Buses' dividend to the council is now being used to get the trams scheme out of a hole, instead of funding key council services."
However, Colin Keir, SNP MSP for Edinburgh Western, said the council had seen sense by agreeing to use its own funds and the agreement would safeguard the use of free bus passes on Lothian Bus services.