Liverpool legend Carragher tweeted simply: "Justice finally. #JFT96"
Another Reds hero, Steven Gerrard posted a picture of the Liverpool memorial with the accompanying message: "JFT 96 #YNWA", alluding to the club's anthem, You'll Never Walk Alone.
Jim Beglin, one of the full backs in Liverpool's squad at the time of the disaster, said: "Disgraceful for 27 years but finally JUSTICE - unlawful killing. Utmost respect for the families courage and determination. #JFT96"
Roy Evans, who played for the club between 1965 and 1974 and then became manager in the 1990s, said: "Finally after 27 years what we've known all along has been confirmed. Thoughts with all the families an those affected. Justice for the 96 x"
Three-time European Cup winning midfielder Terry McDermott said: "At long last we have Justice for those poor 96 souls #ynwa"
Michael Owen said: "Finally and way, way, way overdue, the truth prevails and justice is served."
Another former Liverpool striker, Stan Collymore, tweeted: "J U S T I C E A T L A S T !!!! #JFT96"
Chief executive Ian Ayre released a statement later in the day hailing the 'humbling and inspirational' Hillsborough families and their 'tireless campaign'.
"After 27 long years the true verdict has finally been delivered, confirming what the families always believed - their loved ones were unlawfully killed," he said.
"Liverpool Football Club welcomes the jury's decision, once and for all, that our supporters were not in any way responsible for what happened at Hillsborough. We will always remember the selfless bravery and heroism of the many fans that helped their fellow supporters in the most harrowing of circumstances that day. We praise those who, since the beginning of the inquest, have had to find the courage and strength to re-live what they went through.
"Since April 15, 1989, the solidarity shown by Liverpool fans towards the families and survivors encapsulates the unique character of both the club and city. We are also hugely thankful for the unwavering support the wider football community has so generously shown these past 27 years.
"It has been a painful journey for the families and survivors, who have endured and sacrificed so much for so long. The resilience and dignity they have shown throughout their tireless campaign has been humbling and inspirational. Their conduct and actions throughout their struggle has brought pride to the city of Liverpool and will serve as a lasting tribute to the victims.
"The 96 men, women and children who were unlawfully killed at Hillsborough will never be forgotten."
Everton put their rivalry with Liverpool to one side to release a statement showing Merseyside stood as one over Hillsborough.
"Everton Football Club salutes the Hillsborough families and their total vindication as Fighters for Justice.
"Theirs is the greatest victory in the history of football.
"RIP, the 96. Good night, God bless.
"From us across the Park."
Former manager Rafa Benitez, who is beloved by many Liverpool fans after lending his support to the families campaigning for justice, also released a statement.
Benitez donated £96,000 to the Hillsborough Family Support Group in 2010 a week after his reign as Liverpool manager ended. The Spaniard was also spotted in tears at the Hillsborough memorial in 2011 when thousands turned out at Anfield to pay their respects to those who died in 1989.
The Newcastle United boss said: "After so many years fighting for justice I am really pleased to see the verdict today, which confirms what we have been saying for a long time.
"I am especially pleased for the families of the 96 who have sought justice for so long and with such dignity, as well as for the people of Liverpool and for football fans in general.
"Hopefully this verdict today will ensure that this kind of tragedy can never happen again."
The jurors were told they could only reach that determination if they were sure of four "essential" matters concerning the deaths at the 1989 FA Cup semi-final.
They had to be convinced that overall match commander Chief Superintendent David Duckenfield owed a duty of care to those who died in the disaster, and that he was in breach of that duty of care.
Thirdly, they would need to be satisfied that his breach of duty caused the deaths and, fourthly, that it amounted to 'gross negligence'.
They concluded it was unlawful killing by a 7-2 majority.
The conclusion was greeted with sobbing and cheers at the hearing in Warrington.
The jury also ruled that fan behaviour did not cause or contribute to the tragedy.
The Hillsborough disaster unfolded during Liverpool's cup tie against Nottingham Forest on April 15 as thousands of fans were crushed at Sheffield Wednesday's ground.
Mr Duckenfield gave the order at 2.52pm to open exit Gate C in Leppings Lane, allowing around 2,000 fans to flood into the already packed central pens behind the goal.
Joey Barton, Burnley's former England midfielder who was born in Liverpool, said: "The verdict today owes itself to the iron will and spirit of the family members, survivors and the people of Liverpool. A refusal to yield.
"Proud to be a scouser today. Gone but never, ever forgotten! #JFT96"
John Arne Riise, who won the Champions League with Liverpool in 2005, said: 'Well done to everybody who has been fighting for this the last 27 years! You guys are amazing! Today you got your reward! Truth is out! #JFT96'
Kelly Cates, the broadcaster and daughter of the legendary Kenny Dalglish, who was Liverpool manager on the day of the Hillsborough disaster, said: 'The 96 people who were unlawfully killed, the traumatised survivors. It was not your fault. It never was. And we knew that. #TheTruth.'
Andy Burnham, the MP for Leigh who has been outspoken on the Hillsborough disaster, called the original verdict "the greatest miscarriage of justice of our times."
"After 27 long years, this is real justice for the 96, their families and all Liverpool supporters. The survivors of this tragedy can finally be remembered for what they were on that day - the heroes of Hillsborough who tried to help their fellow fans.
"The Hillsborough Independent Panel gave us the truth. This Inquest has delivered justice. Next must come accountability. For 27 years, this police force has consistently put protecting itself above protecting those hurt by the horror of Hillsborough. People must be held to account for their actions and prosecutions must now follow.
"Disgracefully, lawyers for retired police have attempted to continue the cover-up in this courtroom."
The jury also found that both the police and the ambulance service caused or contributed to the loss of lives in the disaster by an error or omission after the crush in the west terrace had begun to develop.
After the key conclusions were delivered, someone in court shouted "God bless the jury".
The jurors were given a round of applause as they left the courtroom.
Lawyers acting for relatives of the victims said the jury's conclusions had completely vindicated the bereaved families' tireless 27-year fight for justice.
The jury of six women and three men gave their decisions on an emotionally charged day for relatives of the 96, many of whom were at court for the conclusion of the longest jury proceedings in British legal history.
Last Wednesday the jury indicated to the court in Warrington that unanimous decisions had been reached on every question apart from question six - unlawful killing.
They were given a majority direction yesterday and quickly indicated they had reached a majority decision on the outstanding question.
The fresh inquests began on March 31, 2014, in a specially built courtroom in Warrington.
The 1991 accidental deaths verdicts from the original inquests were quashed following the 2012 Hillsborough Independent Panel report after a long campaign by the families of the dead.
Dozens of relatives of the victims have attended each of the more than 300 days the court has sat at Bridgewater Place on the Cheshire town's Birchwood Park business park.
At the start of the inquests, the coroner said none of the victims should be blamed for their deaths.
Emotional tributes to each of the 96 were then delivered by family members in the form of personal portraits.