The long-mooted work was announced yet again yesterday with the Minister saying that the Cabinet had signed off on the cash.
The Green Line terminates at St Stephen's Green and the Red Line runs to the O2 in Dublin's docklands, via Connolly Station, but the two services are not linked.
The new 5.6km cross-city route will remedy this, extending the Green Line to O'Connell Street and providing an interchange with the Red Line at Abbey Street.
Called Luas BXD, the new track will continue north as far as Broombridge, near Cabra.
Mr Varadkar said initial work will begin next May, with the main phase to start in 2015. A selection of city monuments, including Molly Malone, will be moved in the coming months to prepare for the work.
The Cabinet has taken a decision to approve an updated "business case" for the project.
Mr Varadkar will now ask the National Transport Authority (NTA) and the Railway Procurement Agency (RPA) to hire contractors so that the plan can proceed in 2013.
"This is an important step for the Luas BXD project, which will link up the existing Luas lines and give Dublin an integrated commuter rail network for the first time," he said.
"The two Luas lines should have been joined up years ago. It's a privilege for me as Minister for Transport to be able to finish the job.
"Every effort will be made to minimise the impact of construction works on the business community, road users, pedestrians and residents in the city centre area."
It is hoped the project will generate up to 800 jobs during the construction phase, with a further 60 permanent jobs when the line opens.
A new bridge being built over the river Liffey will take the southbound BXD track from Marlborough Street to Hawkins Street.
Among the stops on the new line will be the planned DIT campus in Grangegorman in Dublin 7.
Already, a traffic plan for the St Stephen's Green area is being devised to help prevent congestion when the works begin next year.
A Project Forum, to be chaired by the Transport Minister, will be established to help iron out issues as they arise.
An Bord Pleanala granted permission for the project earlier this year.
It is expected the new line will help push Luas passenger numbers to the 40 million mark.
The new track will go through the city centre, linking up with the Red Line at the junction of O'Connell St and Abbey St.
It will then go to Broombridge where it will link up with the Maynooth commuter rail line.