Tsarnaev looked down and rubbed his hands together as the judge pronounced his fate.
The apology came after Tsarnaev listened impassively for about three hours as a procession of victims and their loved ones lashed out at him for his "cowardly" and "disgusting" acts.
"He can't possibly have had a soul to do such a horrible thing," said Karen Rand McWatters, who lost a leg in the attack and whose best friend, 29-year-old Krystle Campbell, was killed.
The outcome of the proceedings was never in doubt: The judge was required under law to impose the jury's death sentence for the April 15, 2013, attack that killed three people and wounded more than 260.
The only real suspense was whether Tsarnaev would say anything when given a chance to speak near the end of the proceedings.
Until Wednesday, he had said almost nothing publicly since his arrest more than two years ago, offering neither remorse nor explanation.
During his trial, he showed a trace of emotion only once, when he cried while his Russian aunt was on the stand. And the only evidence of any remorse came from Sister Helen Prejean, a prominent death penalty opponent, who quoted him as saying of the victims: "No one deserves to suffer like they did."
In condemning him to death, the jury cited his lack of remorse as one of many factors.