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The move took place in recent weeks and is expected to be confirmed on Monday by the INLA and General John de Chastelain, head of the IICD.
The INLA was a small, ruthless group which killed more than 120 people, including Tory MP Airey Neave in 1979.
In October, it said it would pursue its aims by exclusively peaceful means.
The republican paramilitary group is believed to have been responsible for 111 murders from its formation in 1975 until its ceasefire in 1998, but it is still thought to have been involved in a number of murders since then.
As recently as February 2009, the INLA claimed responsibility for the murder of a drug dealer in Londonderry.
It came to world prominence in 1979 with the murder of Conservative Northern Ireland spokesman Airey Neave by leaving a bomb under his car in the House of Commons car park.
It was behind one of Northern Ireland's worst atrocities when it killed 17 people in a bomb attack on the Droppin' Well pub in Ballykelly, County Londonderry, in 1982.
The group's political wing, the Irish Republican Socialist Party held a parade in Bray, County Wicklow, four months ago and announced that the organisation had renounced violence.
At present paramilitaries moving weapons can use a certificate from the Independent International Commission on Decommissioning (IICD) saying they are moving arms from one cache to another to facilitate decommissioning.
On 9 February, the legislation that allows the IICD to operate ends and any weapons found after that date can be forensically tested.
Evidence from this could be used in future court cases and possibly help secure convictions.
Last month the loyalist paramilitary group th Ulster Defence Association also decommissioned.
The government had made it clear to the UDA that after the legislation expired that they would be treated as common criminals that the police would actively seek their weapons.