In 29 days' time, they will be stopping along the truncated route from York Place in the capital's centre to Edinburgh Airport.
Sources say the launch will be on Saturday, May 31, with the date due to be officially announced by Transport Minister Keith Brown and officials at the Gyle Centre tram stop this morning.
The overall project has cost £776 million, though it is years behind schedule and millions of pounds over the original budget.
The route is a fraction of that originally planned. When the project first started in 2008 the trams were intended to run from the airport to the city centre and on to Newhaven, around two miles north of the city centre between Leith and Granton.
It was cut amid controversy over the project's spiralling budget and delays.
A second line running from Haymarket to Granton Square was postponed indefinitely, and a further proposal for a line serving the south side was not approved by the Scottish Parliament, meaning only one-third of the planned infrastructure has been built.
In 2011 the council considered scrapping the trams before deciding to cut the route even further, running from the airport only as far as Haymarket.
But the Scottish Government threatened to withdraw funding and the stretch from Haymarket to the city centre was restored.
The trams were originally supposed to launch in 2011 and the final cost is an estimated £776m, more than double the £375m cost estimated in 2003.
Transport Minister Keith Brown, the chief executive of Transport for Edinburgh Iain Craig, and Lesley Hinds, the transport convener for Edinburgh city council, are expected to name the passenger launch date this morning at the Gyle Centre tram stop.
Pensioners with concessionary cards will be able to travel free on the trams, while passengers will be able to use the same travelcards on both the trams and Lothian bus services.