On behalf of all 43 forces, police chiefs have promised "cultural change".
They admitted "policing got it badly wrong" in the aftermath of the fatal stadium crush and said a range of key lessons had been learned.
BBC reports ninety-seven Liverpool supporters died as a result of the April 1989 disaster at Sheffield's Hillsborough ground.
The National Police Chiefs Council and the College of Policing published a joint response to a report published in 2017, which consulted the families.
It is the first reply from a major public body to the report, published by former Bishop of Liverpool James Jones.
In his 117-page report, he said: "The experience of the Hillsborough families demonstrates the need for a substantial change in the culture of public bodies."
Bishop Jones said "a change in attitude" was needed to ensure the "pain and suffering" of the families - who spent decades fighting for justice - was not repeated.
He also called for a charter for bereaved families, the right to publicly-funded legal representation and a "duty of candour" for police officers, amid a series of other recommendations.
In response, Chief Constable Andy Marsh, the College of Policing's chief executive officer, said: "For what happened, as a senior policing leader, I profoundly apologise. Policing got it badly wrong."
The National Police Chiefs Council and College of Policing said the code of ethics used by forces would be reviewed, with a duty of candour becoming a key theme.
Bishop Jones had said the response of South Yorkshire Police to criticism over Hillsborough showed "institutional defensiveness" and recommended training for senior officers to ensure an "open and transparent approach" to inquiries.
A first inquest verdict of accidental death, which the families campaigned against for more than 20 years, was quashed in December 2012.
In 2016 a new inquest jury found the victims had been unlawfully killed due to gross negligence manslaughter by the police match commander Ch Supt David Duckenfield.
And, last year, the South Yorkshire and West Midlands police forces agreed to pay damages to more than 600 people over a cover-up which followed the disaster.