David Crompton said relatives of those who died had been failed, and that officers “will now take time to carefully reflect on the implications of the verdicts”.
He read a contrite statement to waiting journalists and camera crews outside the force’s headquarters in Sheffield, but did not take questions.
As the chief constable he spoke, a Labour MP called for his force to be shut down and reconfigured.
Bassetlaw MP John Mann said: “Nobody should pre-judge ongoing inquiries into the police, but whatever conclusions they reach, the credibility of the institution of South Yorkshire Police has been irreparably damaged.
“It needs a new identity and more importantly a new ethos and ethics. South Yorkshire Police should be disbanded.”
Speaking outside the South Yorkshire Police building in Carbrook Hill, Mr Crompton said: “I want to make it absolutely clear that we unequivocally accept the verdict of unlawful killing and the wider findings reached by the jury in the Hillsborough Inquests.
“On April 15, 1989, South Yorkshire Police got the policing of the FA Cup semi-final at Hillsborough catastrophically wrong. It was and still is the biggest disaster in British sporting history. That day 96 people died and the lives of many others were changed forever. The force failed the victims and failed their families.
“Today, as I have said before, I want to apologise unreservedly to the families and all those affected.”
There are two ongoing criminal investigations into the Hillsborough disaster - focusing on the tragedy itself and allegations of corruption in the aftermath - that are expected to be completed in December or January.
Mr Crompton went on: “These inquests have been the longest inquests in British legal history, with nearly 300 days of evidence heard. Whilst these have been lengthy and difficult proceedings, they have once and for all provided a fresh opportunity to explore all of the available evidence about what happened. This has enabled the jury to reach the verdicts that they have today.
“The Hillsborough disaster changed the way in which major sporting events are policed and very many lessons have been learnt. With improvements in training, communications and technology, it is almost impossible to consider how the same set of circumstances could arise again today. We will now take time to carefully reflect on the implications of the verdicts.
“We recognise that this is an important day for the families of those who died at the Hillsborough disaster and for everyone affected by what happened. They have waited 27 years for this outcome. Our thoughts are with them.”
The South Yorkshire force has seen an unprecedented series of controversies, both before and since the Hillsborough tragedy. It came under heavy fire for its handling of the confrontation on the miners’ picket at Orgreave coking plant in 1984, and more recently for its handling of child grooming scandals in Rotherham and Sheffield.
South Yorkshire’s police and crime commissioner admitted there was “nothing that can do justice to the magnitude of failure” in the wake of today’s verdicts.
In a statement released after a jury in Warrington returned verdicts of unlawful death for all 96 victims of the football disaster, Dr Alan Billings, South Yorkshire Police and Crime Commissioner, said he hopes the verdict will answer questions of what happened in 1989.
He acknowledged: “South Yorkshire Police failed the 96 families in 1989. The Force has today, quite rightly, repeated the apology it made in 2012.
“There is nothing that can do justice to the magnitude of the failure.
“We can only hope that these verdicts today contribute in some way to the healing that the grieving families need and that has been denied them for so long.”
Dr Billings added: “My task is twofold: to ensure that past errors are admitted and the Force learns what needs to be learnt; but also to continue to encourage today’s Force to work to the highest of standards, since that is the only way they can accept the past while not being overwhelmed by it.”
Meanwhile, a Sheffield firm of consultant engineers has apologised for its failings surrounding the safety of Hillsborough stadium prior to the disaster - but distanced itself from the company’s role 27 years ago.
The inquests’ jury concluded Eastwood & Partners should have done more “to detect and advise on any unsafe or unsatisfactory features of Hillsborough stadium which caused or contributed to the disaster.”
The company acted as Sheffield Wednesday’s consultants on the stadium’s design in 1989 and remains in the same role today.
In a statement, managing director Philip Richardson said: “We fully respect the inquest’s findings and will study them carefully.
“We have fully supported and followed the inquest and all inquiries from the outset.
“We would like to say sorry on behalf of the company at that time and to add our deepest sympathies to all those affected by this tragedy. We would also like to add that we are a very different company today and there is no-one here who has any first-hand knowledge of the stadium design decisions concerning Hillsborough in the 1980s.
“This was a terrible, tragic incident that will never be forgotten and out of the disaster there has come a legacy of improved stadium safety throughout the country.”