Councillors in the Borders and Dumfries and Galloway have agreed in principle to a Scottish government deal which would see council tax frozen.
The offer would limit budget cuts for the authorities to 2.6%.
That translates to about £6m in the Scottish Borders and a little short of £15m in neighbouring Dumfries and Galloway.
Failure to agree the Holyrood deal could have seen funding to the councils reduced by 6.4%
As well as agreeing to the tax freeze, the authorities had to commit to protecting police numbers, continuing free personal and nursing care for the elderly and protecting teacher posts.