Ice cream seller Mahmoud Bazzi, 71, is to be returned to his homeland where he could ultimately stand trial for the abduction, torture and double killings while serving with a Christian militia.
Privates Derek Smallhorne and Thomas Barrett were on duty with the UN Interim Force in Lebanon (Unifil) near the Israeli border on 18 April, 1980 when they were captured.
They had been in a three-vehicle convoy that was stopped by the South Lebanese Army (SLA) which was controlling the war-torn region at the time and in conflict with the Palestinian Liberation Organisation (PLO).
Tensions were high in the area on the day of the attack as the peacekeepers moved supplies to a border post.
Twelve days earlier, clashes between the SLA and Dutch and Irish soldiers serving with the UN left an Irish man and a member of the militia dead.
The SLA had vowed to avenge the killing.
Two eyewitnesses, Associated Press journalist Steve Hindy and former UN peacekeeper John O'Mahony from Scartaglin, Co Kerry, have spoken publicly about how the abduction unfolded.
Private Barrett, 30, from Cork, and Private Smallhorne, 31, from Dublin, were both married with three children.
They were last seen alive in the back of a car driven by SLA militia men as it sped off after the troops were confronted and involved in shoot out.
The men's families have pursued successive Irish Governments to pressurise the US authorities to act against Bazzi for years.
US Immigration and Customs Enforcement declined to comment on the murder case or whether Bazzi will be charged on his arrival in Lebanon. But a spokesman has said the "allegations of what happened in Lebanon factor heavily in our investigation and our efforts to remove him".
He was arrested last month in Dearborn, a community with a strong Middle Eastern population just outside Detroit, Michigan, where he has earned a living driving an ice cream van.
At a hearing in an immigration court on Monday the Lebanese native admitted entering the US in 1994 without proper documentation and providing false information to authorities that helped secured permanent resident status.
The court heard Bazzi lied to obtain lawful immigration status in the country.
The Irish Government has been following developments in the Bazzi deportation case and a representative from the Irish embassy in Washington DC was due to be in court to observe informally.
The US Department of Homeland Security was being kept up to speed with Irish interest in the case, the Department of Foreign Affairs said.
No date for the deportation was confirmed.
Smallhorne and Barrett are among 47 Irish soldiers who have been killed serving in the UN peacekeeping force since 1978.
Bazzi had been investigated by US Immigration and Customs Enforcement's (ICE) Homeland Security Investigations (HSI). He had originally been traced to the Detroit area by an RTE Prime Time investigation in 2000.
Marlon Miller, special agent in charge of HSI Detroit, said: "One of the agency's highest priorities is to ensure that our nation's immigration system is not exploited by those who seek to illegally gain refuge in the United States by concealing their past.
"We aggressively investigate individuals who enter this country under false pretenses, especially those who hide or misrepresent critical information about their past."
A statement issued by the US embassy in Dublin confirmed Bazzi's court appearance.
The ICE authority said its Human Rights Violators and War Crimes Center investigates those involved in war crimes, genocide, torture and extrajudicial killings who try to evade justice by seeking shelter in the US.
Since 2004, the agency has arrested more than 270 individuals for human rights-related violations under various criminal and/or immigration statutes.
It also secured deportation orders and physically removed more than 650 known or suspected human rights violators.