The widow of Ian Tomlinson said that an apology and settlement from Scotland Yard is "as close as we are going to get to justice".
In a statement, the Metropolitan Police says all the litigation between the Commissioner and the Tomlinson family has been resolved.
The police officer cleared of killing Ian Tomlinson will be sacked after being found guilty of gross misconduct at a disciplinary hearing.
The family of Ian Tomlinson - who died after being pushed to the ground by a police officer during a protest in 2009 - have accepted an apology and undisclosed damages from the Metropolitan Police.
Ian's widow Julia described the out-of-court settlement as "as close as we are going to get to justice".
Ronke Phillips has more.
Ian Tomlinson's widow Julia said:
"Today's apology and admission by the Metropolitan Police that their officer unlawfully killed Ian marks the end of our campaign and legal case.
"On April 1 2009 when we first heard news of Ian's death we simply wanted to know what had happened. We were completely in the dark until a week after his death when we saw the video capturing the violent assault on him by PC Harwood.
"It was, and still is a shocking video. We knew that Ian had been unlawfully killed by the officer as soon as we saw the video, but we had to first go through the long legal process of taking apart untruthful accounts given by PC Harwood and other police officers. We should not have had to do this.
"The last four years have been a really hard uphill battle. We have had to deal with many obstacles and set backs. After the 'unlawful killing' verdict at the inquest it was unimaginable to us that PC Harwood could be acquitted of the criminal charge of manslaughter.
We will never understand that verdict, but at least today's public admission of unlawful killing by the Metropolitan Police is the final verdict, and it is as close as we are going to get to justice.
"It will always be painful for us that Ian died so violently, but at least he is at rest now, and the force has publicly acknowledged the truth. We hope that lessons have been learned and that other families will be spared the tragedy and ordeal that we have had to face.
We loved Ian and will always keep his memory alive by talking about him and sharing our memories with each other as we finally start looking to the future again."
Julia Tomlinson, the widow of Ian Tomlinson, who died after being pushed to the ground by a police officer during the G20 protests in 2009, said Scotland Yard's apology is "as close as we are going to get to justice" and said the family can "finally start looking to the future again".
Scotland Yard today apologised to relatives of Ian Tomlinson, who died after being pushed to the ground during protests in 2009, as it confirmed that an out-of-court settlement has been reached with his family.
The 47-year-old was hit with a baton and shoved by PC Simon Harwood during G20 demonstrations in the City of London, and later collapsed and died.
Today the Metropolitan Police paid tribute to the pain that his widow Julia and family have "endured with dignity" since his death.
Deputy Assistant Commissioner Maxine de Brunner said:
"I take full responsibility for the actions of Simon Harwood on 1 April 2009. His actions fell far below the standard we expect from our officers. I accept the finding of the inquest that Mr Tomlinson was unlawfully killed.
"As the jury found, 'at the time of the strike and push Mr Tomlinson was walking away from the police line. He was complying with police instructions to leave Royal Exchange Buildings. He posed no threat'.
Today, I apologise unreservedly for Simon Harwood's use of excessive and unlawful force, which caused Mr Tomlinson's death, and for the suffering and distress caused to his family as a result."
Constable Simon Harwood, cleared of killing Newspaper Seller Ian Tomlinson during the G20 Protests has been sacked from the Met.
The family of newspaper-seller Ian Tomlinson walked out of a hearing, branding it "a whitewash".
Mr Tomlinson died after being pushed to the ground by Constable Simon Harwood during the G20 riots in central London three years ago.
The hearing by a police disciplinary panel found him guilty of gross misconduct and he has now been sacked.
But the family reacted angrily when the panel said it would not consider if the officer's actions caused or contributed to the death. A trial earlier this year cleared Constable Harwood of manslaughter. Ronke Phillips reports.
Ian Tomlinson's stepson Paul King described the former police officer Simon Harwood's disciplinary hearing as "showboating" and "pointless".
The family of Ian Tomlinson has dismissed police disciplinary proceedings against Pc Simon Harwood as "a whitewash". Speaking outside a police building in Earl's Court, north London, where the hearing took place, Mr Tomlinson's stepson Paul King dismissed the procedure as "showboating".
I think it's pointless, it hasn't proved anything to us. We still haven't got any answer from this. After three-and-a-half years, I think its diabolical. It's like we're back at day one. We will carry on, it isn't going to be the last of it.
He said there was "no justice" in the fact that Harwood now faces the sack. The family are planning to take civil action over Mr Tomlinson's death. Harwood admitted that his actions and the way that they were reported had caused discredit to the Met, and this amounted to gross misconduct.
Former Pc Simon Harwood will keep his police pension despite being sacked for gross misconduct.
Metropolitan Police Deputy Assistant Commissioner Maxine de Brunner said because he has not been convicted of a criminal offence he can claim the payouts when he reaches the eligible age.
– Metropolitan Police Deputy Assistant Commissioner Maxine de Brunner
Simon Harwood will retain his pension when he reaches pensionable age. I'm unable to remove his pension because he has not been convicted of a criminal offence.
Ms de Brunner said it was "certainly worth debating" whether the rules should be changed.