Breaking two years of silence, Boston Marathon bomber Dzhokhar Tsarnaev spoke out and apologised to his victims and their families just before a judge handed his death sentence.

"I am sorry for the lives that I've taken, for the suffering that I've caused you, for the damage that I've done—irreparable damage," said the former college student before a hushed courtroom on Boston on Wednesday.

Tsarnaev, now 21, is set to die by lethal injunction as meted by the federal jury last month for the attack he and his brother Tamerlan carried out in 2013.

On Thursday, Tsarnaev was moved to a US penitentiary in Florence, Colorado, home to the so-called "Supermax" unit that houses high-risk prisoners, a spokesman for the Bureau of Prisons said.

The Tsarnaev brothers detonated bombs placed inside two pressure cookers near the finish line of the 2013 Boston Marathon that killed three people and injured 264. Their stated motive, revealed in court, was to wreak vengeance for the US actions in Muslim countries.

Tsarnaev appeared on Wednesday before US District Court Judge George O'Toole, Jr. He made his verbal apology after listening placidly for almost three hours as 24 victims and survivors angrily lashed at him for his crime, asking him to at least show remorse for what he had done.

"All those who got up on that witness stand and that podium relayed to us, to me — I was listening — the suffering that was and the hardship that still is, with strength and with patience and with dignity," he haltingly told the victims in Russian-accented English.

Tsarnaev's redress was full of religious references and praise for Allah, whom he pleaded for forgiveness. He also asked for Allah to forgive his brother, Tamerlan, who died in a gunfight with the police. He paused several times as if trying to be calm but looked only at the judge despite addressing himself to the victims.

He confessed his crime: "If there's any lingering doubt about that, let there be no more."

"I did do it along with my brother," he added.

Judge George O'Toole Jr., who had to pronounce his death sentence which the jury decided on last month, quoted Shakespeare after Tsarnaev spoke.

"The evil that men do lives after them. The good is often interred with their bones," said the magistrate.

"So it will be for Dzhokhar Tsarnaev," he said, telling the convicted that no one will remember the good deeds he did.

"What will be remembered is that you murdered and maimed innocent people and that you did it wilfully and intentionally."

Families of the victims, on the other hand, said Tsarnaev consciously "chose destruction and hate."

The young man could have opted not to join in the attack and stopped his sibling, said Bill Richard, father of 8-year-old Martin.

"He could have changed his mind the morning of April 15, 2013, walked away with a minimal sense of humanity and reported to authorities that his brother intended to hurt others," Richard said. "He chose hate. He chose destruction. He chose death. This is all on him."

He said he would have preferred for Tsarnaev to receive a life sentence so he would have "a lifetime to reconcile with himself what he did that day."

Patricia Campbell, mother of 29-year-old Krystle Campbell who was killed, said what Tsarnaev did to her daughter is "disgusting."

"I don't know what to say to you. I think the jury did the right thing," she said.

Liz Norden, whose two adult sons each lost a leg during the attack, agreed with the death sentence.

"There are no winners today, but I feel justice for my family," she said. "I have to watch my two sons put on a leg every day. So I don't know about closure. But I can tell you it feels like a weight has been pulled off my shoulders."

Henry Borgard, a survivor, said of Tsarnaev's apology: "I was actually really happy that he made the statement. I have forgiven him. I have come to a place of peace and I genuinely hope that he does as well."