The details of the payments will be determined by an independent panel led by a judge, President Jacob Zuma said.
Police shot dead 34 miners at the Lonmin platinum mine, claiming they were acting in self-defence.
The shooting was the most deadly police incident since the end of apartheid in 1994, and shocked the nation.
The families' lawyers have reportedly welcomed the president's announcement.
"We welcome that process. In fact, that gesture was expected a long time ago by families who had lost hope," the Sowetan newspaper quotes lawyer Tsepiso Ramphele as saying.
They have already filed suits claiming compensation for loss of income and medical costs.
Marikana: 'My husband died in vain'
Marikana mine massacre casts long shadow
Many of the mineworkers who died were sole bread-winners and the compensation will be a welcome relief for their families, says the BBC's Pumza Fihlani in Johannesburg.
Opposition parties argue that the matter should be brought to parliament so they can weigh in on what a fair settlement would be.
In the days before the shooting, 10 other people died at the site, including non-striking miners, security guards and two police officers who were hacked to death.
An enquiry set up by President Zuma sat for two years and looked at the roles played by the police, the management of the platinum mine, Lonmin, the unions and government.
The Farlam Commission found that the police had a "defective" plan to break up the strike and concluded they were wrong to proceed with it.
It recommended a criminal investigation into police over the deaths but no-one has been charged or held responsible for the killings.
Numerous calls have been made for police commissioner Riah Phiyega to be sacked over the incident.
The enquiry criticised both the mining unions and Lonmin for not doing enough to resolve the dispute in the early days of the protests.
There has been no reaction from Lonmin yet on the government's move.
South Africa's government says it will pay compensation to the families of mineworkers killed during a wage dispute in Marikana in 2012.