The awards have been made to 18 former residents at orphanages run by the Congregation of the Poor Sisters of Nazareth in Glasgow, Aberdeen and Kilmarnock and are likely to open the floodgates for criminal-injuries payments to scores of others.
The victims come from all over Scotland and suffered a catalogue of abuse in the homes during the 1960s, 1970s and 1980s.
About 100 people who attended the homes have applied to the Criminal Injuries Compensation Authority (CICA) for payouts.
Further payouts are now expected to the remaining claimants over the next few months.
The decision to award money to the first applicants - who have received between 1,000 and 7,500 - is a major boost in a wider legal campaign for justice led by the former residents, who have taken the Roman Catholic order to the Court of Session to seek damages and an acknowledgment of guilt.
The campaign suffered a major setback when the court ruled that the alleged abuse took place too long ago.
But that "time bar" ruling has been appealed and will be reviewed by judges in January.
One of those who was yesterday told she would receive compensation, Adeline Spence, 43, from Glasgow, said she was pleased with the award, but would not be happy until the Catholic Church admitted the abuse.
"I'm really pleased that the criminal- injuries board has, at long last, acknowledged that we are victims.
"The Catholic Church has admitted guilt in America, Australia, Canada and Ireland. It's like Scotland doesn't exist - they won't admit their guilt to us."
Ms Spence, who was sent to the Glasgow home in 1966 when she was three, described the abuse she suffered at the hands of nuns as "horrific".
She said: "It wasn't until I left that I realised you didn't beat people up, that you weren't forced to eat your own vomit, that your nails were not cut so close to the quick that your fingers bled.
"If you wet the bed they would make you wear the wet sheet round your body and your wet pants on your head. After a while that stopped, but they made you jump into a cold bath every morning."
She said the behaviour of the nuns had left her with deep emotional scars.
"When you are subjected to these things you become very subservient and let people tread all over you.
"It was only after I left when I was 16 that I realised that these things were not normal. It was the only life I knew."
Ms Spence said that she would ultimately like to see criminal charges pressed against her abusers.
So far only one member of the order, Sister Marie Docherty, has been convicted of abuse against children in Scotland.
In 2000, Sister Marie, also known as Sister Alphonso, was found guilty of four charges of cruelty against young girls at Nazareth House children's homes in Aberdeen and Midlothian.
She walked free from court after the sheriff delivered an admonishment.
The victims' lawyer, Cameron Fyfe, said he hoped the CICA ruling would pave the way for the appeal judges to reopen the case.
He explained that the CICA adhered to "time bar" rules which were more strict than those applied by the Court of Session, but that the body chose to use its discretion and hoped judges would follow suite and find in his clients' favour. The clients have never asked how much they were going to get.
"What really boosted them was the acceptance from a government authority, for the first time, that they were abused. They thought that no-one believed them. People would ask, 'How could a nun do these things?' So this is a massive boost to them," he said.
The order is being defended by lawyers from the Edinburgh firm Simpson & Marwick.
No-one there could be contacted for comment last night.
Two years ago the First Minister, Jack McConnell, issued a public apology to children abused while in Catholic Church homes. In a formal statement to the Scottish Parliament, he made a "sincere and full apology on behalf of the people of Scotland" to those who had suffered physical, emotional and sexual abuse while in residential care.
The Church has previously insisted that it has already apologised for the hurt caused to children in its care, and accused the Executive of "playing catch-up".