The Hillsborough inquest conclusions provide "long overdue justice" for the 96 victims and their families, Prime Minister David Cameron has said.
The longest-running inquest in UK legal history ended on Tuesday when a jury determined the 96 supporters who died at Liverpool's 1989 FA Cup semi-final with Nottingham Forest were unlawfully killed.
The jury also decided the behaviour of supporters played no role in the day's events, delivering vindication for families who fought for a second inquest after the initial hearing of 1990 and 1991 returned 'accidental death' conclusions.
A statement on the Prime Minister's official Twitter page read: "Landmark day as the Hillsborough inquest provides long overdue justice for the 96 Liverpool fans who died in the tragic disaster.
"I would like to pay tribute to the extraordinary courage of Hillsborough campaigners in their long search for the truth."
A separate criminal investigation into the events surrounding Hillsborough, Operation Resolve, has been ongoing since December 2012 and is expected to conclude by "the turn of the year", according to commanding officer Assistant Commissioner Jon Stoddart.
The Crown Prosecution Service will then review all the evidence and make a decision on whether to lay criminal charges.
A statement from the CPS read: "Following the inquests' determinations the CPS team will continue to work closely with Operation Resolve and the IPCC as in due course the CPS will formally consider whether any criminal charges should be brought against any individual or corporate body based upon all the available evidence, in accordance with the Code for Crown Prosecutors."
A statement from the Football Association read: "The FA reaffirms its deep sorrow and regret that these tragic events, which occurred at one of its fixtures, led to the loss of life of 96 football supporters on 15 April 1989.
"The FA's sincere condolences remain with the families and friends of the victims. They have conducted themselves with great dignity throughout these Inquests, during which there has been an exhaustive investigation of the horrific circumstances that took place 27 years ago.
"Ultimately, the Inquests stand as testament to the struggle undertaken by the families so the truth might be brought to light.
"While much has changed since 1989, The FA and English football in general must continue to recognise, remember and learn from the tragedy. In looking forward, it is important we never forget.
"Given the ongoing criminal investigations, there are limitations to what we can say. It is in the interests of all concerned that further consideration of the disaster by the relevant authorities must be allowed to take its course."
Sheffield Wednesday have also released a statement after the inquest jury answered yes to the question: Was there any error or omission by SWFC and its staff in the management of the stadium and/or preparation for the semi-final match on 15 April 1989 which caused or contributed to the dangerous situation which developed on the day of the match?
The jury also answered yes to the question: Was there any error or omission by SWFC and its staff on 15 April 1989 which may have caused or contributed to the dangerous situation that developed at the Leppings Lane turnstiles and in the west terrace?
A club statement said: "First and foremost, we recognise the tireless dedication of the families who have remained dignified throughout this process despite the enormously difficult evidence that had to be heard in detail over the course of the inquests.
"Since the disaster, football has evolved immeasurably, with all stadia and associated safety procedures changing beyond recognition in the intervening years.
"Both the ownership and leadership of Sheffield Wednesday has also changed in this time and we reiterate that the sincere condolences of the current chairman, board of directors and everyone at the club remain with the families of the 96 and our thoughts are with all those affected by the tragic events of 1989.
"Sheffield Wednesday will be making no further comment at this time."