The 33-year-old Fulham midfielder captained his country against Italy in their final group game at the Euro 2012 finals in Poznan on June 18 as he reached three figures.
However, a report claimed that the warm-up game against Hungary on June 4 in which Duff, who announced his retirement from international football last month, played, may not be recognised by FIFA because of a discrepancy with the match officials.
But after contacting both the governing body and the Hungarian Football Association on Thursday, the Football Association of Ireland has confirmed that it has discretion to award caps for the friendly and has done so.
Doubt arose over the presence of assistant referee David Vang Andersen on the touchline.
He is not among the current list of FIFA referees and therefore they are not recognising the game in terms of their ranking coefficients.
An FAI spokesman said: "As an away match, the Hungarian FA was responsible for all aspects of the fixture.
"The Hungarian FA said on Thursday morning that they were unaware of the matter, but have been in contact with FIFA. They said that they intend to continue their discussions with FIFA in order to have the fixture recognised for international ranking purposes.
"They have also confirmed that it is their intention to record the fixture as an international match for the purposes of caps.
"Separately, FIFA confirmed to the FAI this morning [Thursday] that one of the assistant referees who officiated at the match, Mr David Vang Andersen, was not on the current FIFA list of referees and this is the reason why they are not recognising the match for their international ranking coefficient.
"FIFA and UEFA also confirmed this morning [Thursday] that the decision to award a cap is at the discretion of the national association and that they do not keep a central record of caps.
"The Football Association of Ireland has decided that the players who participated in the fixture deserve caps, particularly Damien Duff for the service that he gave to his country.
"Consequently, the Association has informed Damien that it will recognise his status as having earned 100 caps for Ireland."
The game, which was played at the Ferenc Puskas Stadium in Budapest, ended 0-0 on a night when the kick-off was delayed by a spectacular thunderstorm.
It is not the first time the FAI has taken such a decision, having awarded caps to those men who played in the abandoned friendly against England in 1995 when the English FA chose not to do the same.