The extra cash will allow 192 more prisoners to be housed at HMP Kilmarnock and HMP Addiewell in the short term to ease the chronic capacity issues currently facing the Scottish Prison Service (SPS).
It is the first time in around seven years that SPS has been forced to pay for extra capacity at the two private jails.
HMP Kilmarnock is operated by outsourcing giant Serco while HMP Addiewell, in West Lothian, is run by Sodexo.
Scotland’s prison population has rocketed in the past 12 months despite repeated pledges from SNP ministers to reduce it.
HMP Barlinnie in Glasgow - the largest jail in the country - is currently at 50 per cent above its operational capacity.
Scotland’s auditor general, Caroline Gardner, told Holyrood’s public audit committee on Thursday that SPS faced “multiple pressures”, including its revenue budget decreasing in real terms in recent years, an ageing estate, and the significant rise in the prison population.
She said the growth was the result of factors outwith SPS’ control and required “solutions from across the justice system”.
She added: “Despite the aim of the Scottish Government’s justice strategy, Scotland still has one of the highest rates of incarceration in Europe.”
A damning report by the public spending watchdog published earlier this month found Scotland’s prisons are close to breaking point, with overcrowding and rising assaults on staff by inmates posing a threat to “operational safety”.
Stress-related sick rates among prison officers have soared in recent years and the SPS was only able to maintain operations because staff worked increased hours,
A Scottish Government spokeswoman said: “We take very seriously the pressures facing prisons and we have been working closely with SPS to manage the rising population.
“We have already made additional financial provision available to SPS and the budget position is being kept under review.
“While there are financial costs for SPS associated with using additional private sector places, they have a responsibility to accommodate those that are sent to them by the courts.”