At the High Court in Belfast Mr Justice Humphreys said that the settlement represented the “end of a very long process” for the families.
The amounts paid out in each case were not disclosed in court but the judge ordered the MoD to pay legal costs.
A statement from the families said they had secured “significant payment in damages” to the families of Fr Hugh Mullan, Frank Quinn, Joan Connolly, Noel Phillips, Joseph Murphy, Daniel Teggart, Edward Doherty, Joseph Corr and John Laverty.
Last year, a fresh inquest concluded that 10 people had been killed by the British Army at Ballymurphy and that they were all innocent victims.
The shootings, over two days, were part of Operation Demetrius -internment without trial – and were later referred to as Belfast's Bloody Sunday, a reference to the killing of civilians by the same battalion in Derry a few months later.
One victim was shot 14 times, mostly in the back, as he lay already wounded and unable to move. Another was a Roman Catholic priest while a mystery sniper killed one victim by shooting him in the head from long-range.
Prime Minister Boris Johnson issued an apology to the families in the House of Commons for the series of shootings over three days which came in the wake of the introduction of internment in Northern Ireland.
In court Mr Justice Humphreys was told that the cases had been settled by consent.
He said: “Can I congratulate the legal representatives for all their efforts. Lots of people are involved in reaching a conclusion such as this.
“Also to the people for whom these cases have meant a huge amount.
“I have become aware of the significance of these cases in the lives of many people, some of whom are in court.
“This represents the end of a very long process which has seen the inquests go through many months of hearings and ultimately reach the conclusions you are all familiar with.
“Those conclusions have meant that these proceedings have been easier to bring to resolutions.
“As well over 50 years have elapsed since these events occurred I am acutely aware of the significance of today as part of the process that all of you have had to go through.”
A statement from the families said: “The conclusion of this case comes just over a year since the coroner Justice Siobhan Keegan found our loved ones entirely innocent.
“The coroner found the British army responsible for deaths of our loved ones, however as we speak the Ministry of Defence haven’t come forward with an apology.
“We have proven that current legal routes open to all victims of our troubled past do work despite the claims of Brandon Lewis and Boris Johnston to the contrary.
“All victims deserve justice and full access to the courts.”
A compensation claim from the family of the 10th person who died at Ballymurphy and a number of people who were injured are still progressing through the courts.