Speaking at a Policing Board meeting on Thursday, Chief Constable Matt Baggott revealed a PSNI investigation would take place.
He said it will take four years, with 30 skilled officers involved.
The announcement follows the Saville Inquiry, which took 12 years to complete and cost nearly £200m.
The Saville report, published in 2010, found that the civil rights demonstrators shot dead by British soldiers in Londonderry in 1972 were innocent.
Papers were passed to the Public Prosecution Service last November in the wake of the inquiry.
The PPS has now told police they felt there were grounds for prosecution and a full criminal inquiry is due to follow.
But Mr Baggott warned the investigation could divert resources from other areas.
"We understand fully our legal obligations and we are committed to doing this but I need to bring a conversation with the Policing Board in October in order to work through the implications and the consequences," Mr Baggott said.
"I do not think anywhere else in the world is facing the challenges of organised crime, paramilitary activity ... alongside having to deal with 30 years of misery in such a way," he said.
The PSNI has consulted prosecution lawyers and said it will conduct the investigation to the highest standards.
This has to be done to modern standards of murder investigation, which is both resource intensive and prolonged.
Mr Baggott said it is expected to run up a huge bill.
"This will be, and is already, a very long resource intensive investigation which does have implications looking forward to how we are going to be able to sustain this," he said.
"If we prioritise this particular work, and I know how incredibly important this is to people - particularly victims - what are the consequences in relation to protecting and keeping people safe in 2012, 13, 14, 15?" Mr Baggott asked.
"Because I can't ask the people doing this to take on a whole raft of other tasks which may be incredibly serious by themselves."
Bloody Sunday relatives have led a campaign for the soldiers to be prosecuted after the publication of the Saville report.
John Kelly, whose brother Michael was shot dead, told UTV: "The report is totally damning of the parachute regiment in that they unjustifiably murdered our people.
"I feel that it shouldn't take much longer to actually come to the point where these guys should be prosecuted for what they did."
But Sinn Féin's Gerry Kelly, who sits on the Policing Board, said the lack of police resources was "worrying".
"We need to move it forward and I'm worried that we won't move it forward at the pace which is necessary," he said.
"The question that I want answered is when will they move this ahead, and saying that they aren't ready to move it ahead I think will be very worrying for everybody."
"This is a huge issue for the families. People have waited a long time for justice," he added.
UUP MLA Tom Elliott said the news came as "a bolt from the blue".
The party justice spokesperson said: "I am absolutely shocked at this decision which has come as a bolt from the blue."
"Here we see the hierarchy of victims. Those who received a fully funded public inquiry have the Attorney General setting up a murder trial. Those whose loved ones died at the hands of terrorists and who have been denied such an Inquiry are not being afforded equality," Mr Elliott added.
Legacy issues cost around £12.5m per year through the Historical Enquiries Team.