BOSTON (AFP) - A US federal judge formally sentenced Boston bomber Dzhokhar Tsarnaev to death Wednesday at an emotionally-charged court hearing in which the 21-year-old former student apologised to his victims.

Judge George O'Toole officially imposed the death sentence, which had been reached unanimously by the 12-person jury on May 15.

"I would like to now apologise to the victims and to the survivors," said Tsarnaev.

"I am guilty," said the pale and thin former student, making his first public remarks since the 2013 bombings.

"Let there be no doubt about that."

The US citizen of Chechen descent said he had listened throughout the 12-week trial as he learnt about the victims and as survivors gave harrowing testimony.

"I am sorry for the lives I have taken, for the suffering, the damage that I have done," he said, wearing a dark blazer.

He began by delivering his remarks in the name of Allah and finished by asking for God's forgiveness.

"I pray to Allah to bestow his mercy upon the deceased," he said.

"I ask Allah to have mercy upon me, upon my brother, upon my family."

Tsarnaev and his older brother Tamerlan carried out the double bombing at the Boston Marathon finish line, one of the deadliest attacks on US soil since the Sept 11, 2001, attacks.

The two pressure-cooker bombs, hidden in backpacks, killed three people and wounded 264 others, including 17 who lost limbs.

The brothers went on the run and killed a police officer, before Tamerlan was shot dead and Tsarnaev arrested, four days later.

He was found, injured, in a grounded boat on which he had scrawled a bloody message defending the attacks as a means to avenge US wars in Iraq and Afghanistan.

More than 20 victims and their relatives gave emotional statements to the court Wednesday.