The project began on Monday (8 July) and is expected to take around six weeks to complete.
In 2009, the memorial, which commemorates the Midlothian Football Club footballers who lost their lives in World War One, was placed in to storage for safe keeping as tram construction works started in the area.
Over the next six weeks, it will now carefully be rebuilt in the centre of the Haymarket road junction, opposite the Haymarket bar.
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Councillor Lesley Hinds, Transport Convener, said: "This memorial holds a special place in the hearts of many in Edinburgh and I'm delighted work is now beginning to restore it to its rightful place in the centre of the Haymarket junction.
"Tram work continues to progress well along the length of the route - 2013 has been a very productive year so far for the project and I expect that to continue."
David Southern, Managing Director of Hearts, added: "This memorial is one of the jewels in the crown of Heart of Midlothian Football Club and is naturally something that everyone associated with the club is very proud of. We are delighted that it is being re-instated and can once again take its rightful place as one of this great city's prime landmarks."
The contract completion date for the project remains summer 2014.
Once on-street works and overhead cabling work has been completed, a programme of rigorous testing and commissioning will take place to prepare the system and the service for operation.
The tram project team will report to Council in September 2013 with an update on progress.
(JP/CD)
