Derek Chauvin has been sentenced to 22 years and six months in prison for the murder of George Floyd, a crime that shook America and the world.
Delivering the sentence, judge Peter Cahill said the prison term reflected the "particular cruelty" of the killing.
The judge said: "My comments are actually going to be very brief, because most of it is going to be in writing," referring to his sentencing memo.
He said that he will let his written work stand, because this case "is a legal analysis" and "is not based on emotion or sympathy."
Judge Cahill said the pain of the George Floyd murder had been felt around the country, but added: "Most importantly we need to recognise the pain of the Floyd family."
What did Derek Chauvin say?
Earlier, Chauvin himself had addressed the court. He said: "Due to some additional legal matters at hand, I’m not able to give a full formal statement at this time.
"Very briefly though, I do want to give my condolences to the Floyd family.
"There's going to be some other information in the future that would be of interest - and I hope things will give you some peace of mind - thank you."
His mother, Carolyn Pawlenty, had also addressed the courtroom. "My son is a good man," she said, denying that he was a racist.
"Even though I have never spoken publicly,” she added. “I have supported him 100% and always will.”
What did George Floyd’s family say?
The victim's brother, Philonise Floyd, said his life changed forever on 25 May, 2020, adding that he hadn't had a real night's sleep because he is haunted by nightmares of the sound of his brother pleading for his life.
"George’s life mattered," he tells the court, at times wiping away tears.
He told the court that the Floyd family have been given a "life sentence" and "will never be able to get George back".
In an emotional statement, Floyd’s other brother Terrence told the court: "I'm here representing my brother."
"On May 25, 2020, my brother was murdered - everyone knows - by Derek Chauvin."
"What were you thinking?" he asked Chauvin directly.
"What was going through your head when you had your knee on my brother's neck?
"When you knew that he posed no threat anymore, when he was handcuffed, why didn't you at least get up?
"Why did you stay there?"
His sister Bridgett Floyd later released a statement praising the sentencing.
"The sentence handed down today to the Minneapolis police officer who killed my brother George Floyd shows that matters of police brutality are finally being taken seriously," she said.
"However, we have a long way to go and many changes to make before Black and Brown people finally feel like they are being treated fairly and humanely by law enforcement in this country."
A jury found Chauvin guilty of murdering Floyd in April.
The jury unanimously found the former police officer guilty of second-degree and third-degree murder, and manslaughter.
The murder of George Floyd, 46, sparked global protests against police brutality and racism, with a worldwide audience tuning in for the jury verdict earlier this year.
President Joe Biden was among those who hailed the verdict, saying that it "can be a giant step forward in the march toward justice in America".
The three other officers involved in Floyd’s death are Tou Thao, J Alexander Kueng and Thomas Lane. They are each facing two charges of aiding and abetting second-degree unintentional murder and manslaughter.
They are expected to stand trial together in March 2022.
All four officers are separately also facing charges of violating Floyd's civil rights.