On Saturday at 6.50pm, Anthony Creed, of Bawnlea Close, Tallaght, was hit by the tram while crossing the tracks near the Square shopping centre.
He was walking along Cookstown Way, between the Square and Hospital Luas stops, at the time.
Mr Creed was conscious when he was taken to Tallaght Hospital but died in the early hours of Sunday morning. He was in his late 50s and had suffered severe head injuries.
A statement from gardaí yesterday said they were investigating the crash.
Spokeswoman for Luas operators Veolia Transport, Dervla Brophy, said it had begun its own inquiry.
Veolia also confirmed it is the first time a Luas tram had been involved in a fatal accident on either the Red or Green lines during its first four years of operation.
Ms Brophy said Veolia’s sympathies went out to Mr Creed’s family.
“We learned on Sunday that the man who was injured in the incident on Saturday had passed away.
“We commenced an investigation into the incident and naturally we would like to extend our sympathies to the family of the victims,” she said.
It is Veolia’s protocol after all crashes involving a Luas tram to test the driver for alcohol and drugs. Drivers are also put on paid leave while investigations are continuing.
There have previously been two fatal motorcycle crashes near the tramlines during construction, and a number of minor incidents have happened since the service began in June 2004.
In its first full year trams were involved in 38 separate crashes on the two lines.
Last year Luas trams were involved in 28 road crashes and on 18 occasions a tram hit a pedestrian — two people had to be hospitalised.
Last December a man suffered serious head injuries after he was hit by a tram.
Luas drivers had raised concerns about safety on the Red line between Connolly Station and Tallaght in the initial operating period but these were largely alleviated and the frequency of service increased when the number of accidents reduced.
Veolia said there were passengers in the tram at the time of Saturday’s crash but could not make any further comment.
Meanwhile, the woman who died in a crash in Salthill, Co Galway, on Friday last has been named as Aileen Feeney, 22, from Dromore West, Sligo. The car she was travelling in hit a parked truck at 3am.
And a man who died in a crash in Ballymahon on February 18 has been named as Lukasz Jendrysiak, 24. He was a Polish citizen living at Moycourt, Ballymahon, Co Longford.