Garda Commissioner Noel Conroy has told a major North-South police seminar in Dublin that money recovered in Co Cork last February was part of the proceeds of the Northern Bank robbery in Belfast.
Commissioner Conroy said he was satisfied the link has been established, despite the scepticism expressed by Sinn Féin.
"I think if someone is saying that they are very much mistaken. I am satisfied at this stage of the investigation that we will show the money recovered during Operation Phoenix is part of the takings from the robbery of the Northern Bank in Belfast," he said.
During the operation detectives seized an estimated £5 million in sterling notes, in a raid on a bungalow in Farran, Co Cork, in February, and also recovered money which was being burned in the back yard of another house in the county.
Commissioner Conroy refused to say whether the link to the Northern Bank raid last December, which was suspected to be the work of the IRA, had been established through forensic analysis of the notes.
"What I have seen at this stage, I am now satisfied that we will get to that position in the near future," he said.
Although gardaí have expressed their strong belief that such a link existed, Commissioner Conroy's comments are the first official confirmation.
The annual Cross-border cooperation seminar in Dublin involves officers from both the Irish police and the police service of Northern Ireland (PSNI).
PSNI Chief Constable Hugh Orde said that in a way it did not really matter what had happened to the remainder of the money stolen in the Northern Bank raid, the biggest of its kind in British history.
He referred to the decision by the Northern Bank to recall hundreds of thousands of notes from circulation and issue entirely new ones in their place.
"People haven't really recognised the significance of the strategy which by working with the banks rendered it as much use as waste paper. So it wasn't a hugely successful operation bearing in mind the amount of considerable effort the provisional IRA had to put in pulling it off. We suspect a lot of the money may now have been disposed of because its now useless, " he said.
The cross-border seminar was attended by members of the Irish and Criminal Assets Bureau and British Assets Recovery Agency, which has recently mounted joint operations against the suspected assets of alleged IRA Chief Of Staff Tom "Slab" Murphy.
The head of the ARA Alan McQuillen said it was impossible to estimate the size of the IRA's criminal assets, given the organisation's 25-year history.
But he said that all of the agencies involved were working to identify the assets and to take them out of circulation.