He was shot as he drove to work on the M1 in County Armagh on 1 November.
The new paramilitary group is believed to have been formed from an amalgamation of previously disparate dissident republican organisations.
In a statement issued to the Belfast-based newspaper, the Irish News, the group said it killed him “to protect and defend” republican prisoners.
Mr Black was driving to work at Maghaberry Prison, Northern Ireland’s high security jail, when he was attacked and killed.
There is an on-going dispute at the prison, where 41 dissident republican prisoners are detained.
Many of them are refusing to wash in protest at strip searches, and in a bid to secure political status.
Mr Black, a 52-year-old father of two, was the first prison officer to be murdered in Northern Ireland in almost 20 years.
A new organisation calling itself the IRA was formed during the summer, bringing together the Real IRA, Republican Action Against Drugs, and a group of non-aligned republicans – a number of whom are believed to be based in the Craigavon area of County Armagh.
