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.
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.