In the 1980s the toppled dictator sent large quantities of arms and explosives to Ireland to be used by republicans.
DUP Lagan Valley MP Jeffrey Donaldson said Semtex from the shipments was used during atrocities such as the 1993 IRA bombing of Warrington, Merseyside.
"I don't think anybody will be comforted but there will be widespread relief that this has happened and that we finally see an end to his evil regime," Mr Donaldson said.
"This now clears the way for what we hope will be the conclusion of our negotiations with the new government to settle the legal claims which have been made by a small number of IRA victims.
"We will be pressing for the establishment of a fund to assist the wider group of victims who suffered as a result of Gaddafi's sponsorship of the IRA and his arming of the IRA during the earliest years of the troubles."
Two boys, Tim Parry and Johnathan Ball, died in the IRA blast in Warrington. Several other mass killings across the UK were blamed on Libyan arms and Northern Ireland politicians began talks with Tripoli in 2009 to secure compensation for 160 victims of the Provisional IRA.
The victims' group - which acted after Libyan authorities paid 1.5 billion dollars (£918.7 million) to a US compensation fund for victims of the 1988 Lockerbie bombing - has not put a figure on the amount of compensation it is seeking.
The UN Security Council voted to completely lift sanctions against Libya in 2003, but at the time the DUP's Ian Paisley Jr argued against this because of the lack of compensation for IRA victims.
As part of the negotiations to lift sanctions, Libyan officials provided information about millions of pounds and 120 tonnes of weaponry which they had given the IRA. However, the UK government has never secured a compensation deal from Libya for victims of IRA attacks.