The move is seen as vital to getting Stormont's budget on a sustainable footing.
The redundancy scheme formed part of the financial package attached to the Stormont House Agreement.
The Westminster government would allow the Northern Ireland Executive to borrow £700m over four years to pay off up to 20,000 public servants.
A £200m portion would be used to cut up to 3,000 jobs in the Civil Service alone by March 2016.
The agreement was signed in December but fell apart within three months over the vexed issue of welfare reform
In March, Ms Villiers told an audience in Washington DC that the financial package could not go ahead without welfare reform.
But by this weekend, that position was clearly no longer sustainable.
The decision to grant the extra borrowing powers, while the rest of the agreement is not implemented, is simply a recognition of the perilous state of Stormont's finances.
The Northern Ireland Executive is already operating a provisional or 'fantasy' budget - one which assumes that welfare reform has happened when, of course, it has not.
On top of this, Stormont departments have already built the savings from the redundancy scheme into their budgets for the rest of this year.
If the scheme did not proceed, it increased the risk that budgets would be bust right across Stormont.
The head of the Civil Service, Malcolm McKibben, expects that in this financial year the scheme will knock about £25m off his pay bill.
By next year, he said the accrued savings will be £95m to £100m and, in all, he expects the scheme to have paid for itself with 14 months.
Those savings will start almost immediately with the first 864 civil servants due to take redundancy at the end of this month.

Esteban Ruiz Santiago is accused of murdering five people at the Fort Lauderdale-Hollywood International airport on Friday.
During a 15-minute court appearance on Monday he was told by the judge that he may face the death penalty.
Santiago answered the judge's questions in a clear voice.
He spoke very little during the hearing and confirmed to the judge that he understood the criminal charges and that he is a US citizen.
When asked about his employment, he told the judge that he worked for the Signal 88 security firm in Anchorage, Alaska, for the last few years and that he currently has only $5 to $10 in his bank account.
Security was high outside the courtroom, with more than 25 armed police guarding the building.
Santiago wore a red jumpsuit and was shackled at the wrists, stomach and legs throughout the hearing.
Authorities say they have not ruled out terrorism as a motive, and that they are investigating whether mental illness may have played a role in the attack.
In November 2016, Santiago visited an FBI building in Anchorage to tell agents he was hearing voices and believed that US spies were trying to control his mind.
According to a criminal complaint, Santiago told investigators that he flew one-way from Alaska to Florida to carry out the attack.
Agents say he checked a handgun into his luggage.
He retrieved the gun from the baggage carousel, and loaded it in a bathroom before emerging and firing at random, investigators say.
Six other people were wounded by gunshots at the airport's baggage claim area.
Three dozen suffered minor injuries in the chaos as passengers and airport workers fled.
The Northern Ireland Secretary of State Teresa Villiers has said the UK government will release funding to allow a public sector redundancy scheme to go ahead.
[NEXT_CONCEPT]
A 26-year-old Iraq war veteran suspected of opening fire in a crowded Florida airport last week has appeared in court to hear charges against him.