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.

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Mignolet struggled as the Reds twice gave away the lead in a thrilling 3-3 draw with the Premier League leaders.
"For the second goal he needs help from all the players," said Klopp, in reference to Mignolet scrambling as Olivier Giroud scored from a corner.
The Belgium goalkeeper, 27, is set to sign a new five-year contract.
Mignolet, who joined the Reds from Sunderland in a £9m deal in June 2013, was also beaten at his near post by Aaron Ramsey for Arsenal's first equaliser.
Klopp, who has consistently backed Mignolet, added: "On the second goal, on a perfect day he can make a save but there were a lot of mistakes before.
"We have to defend this better."
Liverpool's goalkeeping weaknesses have been exposed by errors from Mignolet's deputy Adam Bogdan in the 3-0 defeat at Watford and the 2-2 FA Cup draw at Exeter.
That has prompted Klopp to recall 22-year-old Welshman Danny Ward, a substitute on Wednesday, from a successful loan spell at Aberdeen.
Liverpool snatched a deserved draw with Arsenal thanks to Joe Allen's late equaliser.
Roberto Firmino twice gave Liverpool the lead in a breathless first half, the second a spectacular 20-yard drive, but Arsenal levelled through Ramsey and Giroud.
Giroud's second-half strike - his 18th goal of the season - looked to have put the Gunners on course for a crucial victory, but substitute Allen rewarded the hosts for a display bursting with energy and spirit with a low 90th-minute finish.
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Klopp was delighted with the performance of Brazil forward Firmino, who has struggled to live up to his £29m transfer fee since arriving from Hoffenheim in the summer.
The German said: "I could talk about this for half an hour. He doesn't know how good he is. If you are good, you have to show it.
"He had a really good game but he was not the only one. I could talk about special performances - we had a lot of other players."
Klopp was also involved in an angry first-half exchange with fourth official Robert Madley and was calmed down, amiably, by his opposite number Arsene Wenger.
He said: "I told Arsene why I was a little bit emotional. It was a clear throw-in for us in a good moment, a good phase. I said what I said, he said what he said.
"We had nothing, it was friendly."
A group calling itself "the IRA" has said it murdered the Northern Ireland prison officer David Black.
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Liverpool boss Jurgen Klopp defended under-fire goalkeeper Simon Mignolet after his latest uncertain display in the draw with Arsenal at Anfield.