Ahern noted that he had been the first European Union minister to call for the closure of the facility in Cuba, which was set up by George Bush, the former US president.
"The [Irish] government has consistently called for its closure since then," Ahern said.
With regard to travel arrangements for the men, he said: "A definite timetable has yet to be established, [but] the transfer of the two detainees is expected within the next couple of months."
Media reports have suggested the two inmates are Uzbek nationals, but a justice ministry spokesman declined to comment, and Ahern said the men's privacy would be respected.
Underlining the difficult conditions in which they had been detained for a number of years, Ahern said they would need to be given time and space to adjust to their new circumstances when they arrive.
Obama pledged to close Guantanamo within a year, as one of his first announcements after taking office in January, but questions have been raised over whether it can be achieved.
On June 15, EU foreign ministers agreed a deal with the US on transferring Guantanamo detainees, but stressed that the decision to accept any inmate was one for individual European governments.
On the same day, Obama announced that Italy had agreed to accept three detainees, while Portugal has since said it was ready to take in two or three, and Hungary has offered to accept one or two.
Four detainees of Uighur origin were resettled on the British overseas territory of Bermuda in early June, although it later emerged that London had not been consulted on the matter.
Other countries which have said they may be willing to accept former detainees include Belgium, Britain, France and Spain.
The EU-US agreement stops short of insisting that Washington help finance resettlement operations, noting only that "the United States will consider contributing to the costs incurred by EU member states."
The prospect of transferring the remaining approximately 240 inmates in Guantanamo to top security jails in the US remains deeply unpopular in the US Congress.