John Downey has been granted bail by a High Court judge in Dublin, pending the approval of financial guarantees.
The 66-year-old former IRA man is wanted by prosecutors in Northern Ireland over the 1972 murders of two soldiers in Co Fermanagh.
Downey was arrested in Co Donegal on Monday on a European Arrest Warrant.
Prosecutors in NI have initiated extradition proceedings after announcing they have sufficient evidence to charge him with the murders of Lance Corporal Alfred Johnston, 32, and Private James Eames, 33, in a car bomb attack in Enniskillen.
In 2013, Downey was charged with murdering four Royal Household Cavalrymen in an IRA bomb in London's Hyde Park in 1982.
He stood trial at the Old Bailey, but the case dramatically collapsed after it was revealed he had received a written assurance from former prime minister Tony Blair's government that he was not actively wanted by the authorities.
Explaining the rationale for granting bail on Thursday morning, the judge highlighted that Downey had been on bail during court proceedings in England and had abided by all conditions.
He is expected to walk out of the court building later on Thursday if information the judge has requested on bail guarantees is received.