The Scottish Prison Service is expected to make pay-outs totalling about £500,000 to 300 prisoners forced to slop out while sharing a cell.
Hundreds of prisoners are seeking compensation for slopping out
It has accepted that the practice, used where cells have no integral sanitation, breaches human rights laws.
However, the courts will still have to rule on similar claims from a further 1,100 prisoners held in single cells.
The claims followed the award of £2,400 to Robert Napier two years ago in a landmark judgement.
The Scottish Prison Service (SPS) has decided not to contest the claims of the 300 men who said their human rights had been breached.
They had complained that they were forced to use a potty in a cell which they were sharing with another prisoner.
The other 1,100 cases, which are still before the courts, involve prisoners who were held in single cells.
The Scottish Executive originally claimed that while slopping out was unpleasant and distasteful, it did not breach human rights.
Its agreement to settle the 300 cases involving shared cells will help to cut legal costs, which reached £1.5m in the Napier case.
Slopping out is now confined to 350 prisoners at two jails - Polmont Young Offenders' Institution, where it is due to end next year, and Peterhead, where prisoners have to use chemical toilets because the jail's granite structure makes modern plumbing difficult.
A statement from the SPS said it was now clear, after recent European Court of Human Rights decisions, that slopping out in "doubled-up" conditions was a breach of prisoners' rights.
"SPS is aware of its responsibility to ensure that the large number of slopping out cases already in the courts must be dealt with as efficiently as possible," it said.
"It will therefore be presenting proposals to the Court of Session for the efficient and effective management of these cases, which take account of these recent decisions.
"SPS has instructed legal representatives to make an offer in settlement of all claims where prisoners have been detained in doubled-up slopping out conditions."
It said no offer would be made in cases where the service argued a time-bar applied.
It added that "offers of compensation will only be made to those prisoners who were held in doubled-up slopping out conditions and will be made in line with the levels of award made by the European Court".
SPS said it would continue to contest any claims brought by prisoners alleging a breach of their human rights as a result of slopping out in single cell accommodation.
SNP justice spokesman Kenny MacAskill said: "This is an appalling mess entirely of the Labour-led government's creation.
"They were warned what would happen and have repeatedly failed to act.
"This money could have been used for public benefit elsewhere."
Margaret Mitchell, Conservative justice spokeswoman, said: "The taxpayers of Scotland are paying a heavy price for the inexcusable negligence of the Scottish Executive and the ineptitude of Jack McConnell as finance minister at that time.
"They have to pay twice - once to end slopping out, and then even more to pay compensation to prisoners across Scotland.
"We must not forget that this was an entirely avoidable fiasco."