She spoke in the Commons today after the Crown Prosecution Service announced that six individuals - including four former South Yorkshire Police officers and an ex-lawyer - are to face legal action.
Match day commander David Duckenfield, who was in charge of policing the FA Cup semi-final at Hillsborough on the day of the disaster, has been charged with manslaughter by gross negligence of 95 of the 96 Liverpool FC fans who died.
The CPS said it is alleged that Duckenfield's failures to discharge his personal responsibility were 'extraordinarily bad and contributed substantially to the deaths of each of those 96 people who so tragically and unnecessarily lost their lives'.
Sir Norman Bettison is accused of four counts of misconduct in public office over alleged lies about his involvement in the aftermath of the Hillsborough disaster and the culpability of fans.
Former Chief Superintendent Donald Denton is charged with doing acts with intent to pervert the course of public justice relating to changes made to witness statements.
Former Detective Chief Inspector Alan Foster is also charged with doing acts with intent to pervert the course of public justice relating to material changes made to witness statements.
Peter Metcalf, whoa acted for South Yorkshire Police after the disaster, is charged with doing acts with intent to pervert the course of public justice relating to material changes made to witness statements
Graham Mackrell, who was Sheffield Wednesday's company secretary and safety officer at the time, is charged with two offences of contravening a term of condition of a safety certificate contrary to the Safety of Sports Grounds Act 1975.
In the Commons, Theresa May told MPs: "I know from working closely with the families when I was Home Secretary that this will be a day of mixed emotions for them, but the House will understand that I cannot say anything further on matters that are now subject to a criminal prosecution."
The Prime Minister welcomed the decision by the CPS and praised the 'absolutely exemplary' campaign by the Hillsborough families and others.
She added: "Obviously today will be a day of really mixed emotions for them, but I welcome the fact that charging decisions have been taken. I think that is an important step forward."
At Prime Minister's Questions, Labour leader Jeremy Corbyn said: "This prosecution, the inquiry and this development only happened because of the incredible work done by theHillsborough Justice Campaign, Andy Burnham, Steve Rotheram and other colleagues around this House.
"I think we should pay tribute to all of those that spent a great deal of time trying to ensure there was justice for those that died at Hillsborough."
Assistant Commissioner Rob Beckley, in charge of Operation Resolve, the investigation into the causes of the disaster, said the decision to prosecute came 'after the most detailed and substantial investigation there has ever been into the Hillsborough disaster'.
He added: "Our inquiry looked at all aspects of the event, including the planning and the preparation for the game, the safety of the stadium and the response by the emergency services. "Our inquiry has seen over 17,000 lines of inquiry and we have taken statements off over 11,000 people, from police officers, spectators, emergency personnel and officials from different organisations.
"From our inquiries we referred 12 individuals and three organisations to the CPS for them to consider whether any of these 15 should face criminal action. It was important to us that the CPS were an arbiter of our investigation, applying independent judgment in relation to possible offences.
"Operation Resolve will now continue to work with the Crown Prosecution Service and counsel as the case moves on to the next stage and we prepare for legal proceedings.
"Our work under the Police Reform Act and the allegations of police misconduct remains ongoing and, whilst the criminal prosecutions are foremost in our mind, the publishing of these reports is a very important task for us as they provide a detailed account of the actions of the police on the day.
"We will continue to meet with families of the bereaved and, where appropriate, support and assist them where possible. It is hugely important for me to stress the need for people to respect the criminal process that awaits us."
Ian Lewis, the partner at JMW Solicitors who is representing Duckenfield and Denton, said: "In light of the decision by the Crown Prosecution Service to commence criminal proceedings against David Duckenfield and Donald Denton, it would be inappropriate for me as their solicitor or for my clients themselves to make any comment."
Chief Superintendent Tim Jackson, national secretary of the Police Superintendents' Association of England and Wales, said: "This has been a long and extremely difficult process for everyone involved and our thoughts and sympathies are with the families of those who died in this tragedy.
"Both this association, and those to whom we have provided support, have co-operated fully with the legal process.
"As charges have been brought we will make no further comment."