Privates Derek Smallhorne and Thomas Barrett were on UN peacekeeping duty in Lebanon when they were murdered.
Lebanese national Mahmoud Bazzi, 71, has been sent back to his home country after admitting immigration fraud.
The Irish defence minister said the deportation was a "significant step in the pursuit of justice" for the troops.
A third Irish soldier was injured in the incident near the Israeli border on 18 April 1980.
All three were serving with the United Nations Interim Force in Lebanon (UNIFIL) when their convoy was stopped and they were captured.
Mr Bazzi reportedly entered the United States about 20 years ago and had recently been living in Detroit.
Officers from the US Enforcement and Removal Operations agency escorted him on a flight to Beirut on Friday and handed him over to the Lebanese authorities.
Campaigners are hoping he will be questioned about the soldiers' murders.
Irish Minister for Defence Simon Coveney said: "I believe that this is a significant step in the pursuit of justice for Privates Thomas Barrett and Derek Smallhorne who lost their lives while on United Nations peace-keeping duty in Lebanon almost 35 years ago.
"It is an important day for the families and I wish to commend them for their continued commitment to securing justice for their loved ones."
A suspect in the 1980 murder of two Irish soldiers who were killed on United Nations duty has been deported from the United States to Lebanon.