The final vote by all 56 senators present moves to counter a controversial Supreme Court ruling last week allowing those convicted of such crimes to have their terms trimmed by twice the amount of time they spent in custody awaiting trial.
The law's passage came just ahead of a mass march on the Supreme Court on Wednesday organized by human rights groups protesting its ruling.
Many of the demonstrators raised white handkerchiefs symbolic of the Mothers and Grandmothers of the Plaza de Mayo, an organization that highlights the confiscation of babies born to suspected dissidents during the dictatorship.
"We have shown, once again, that we do not want perpetrators of genocide, rapists and murderers to walk by our side," cried Taty Almeida, a veteran Argentine activist and key member of the Plaza de Mayo group.
Singers, actors, soccer players and politicians of all sides were among the crowd, which organizers said grew to some half a million people, in Buenos Aires.
"We must protest so that they do not dare release the perpetrators of genocide again," said Alba Cervantes, a woman who around her neck wore the photo of her brother who disappeared in 1977.
Similar marches took place in other cities across Argentina, including Neuquen, Cordoba and Rio Negro.
The bill countering the Supreme Court's ruling had passed the lower chamber of Congress on Tuesday with a vote of 211 to 1.
President Mauricio Macri, who must now promulgate the law, said just before the vote that he was "against any tool that helps impunity, especially when it comes to crimes against humanity."
Interim Senate leader Federico Pinedo said the rapid vote "is a very clear message to society and to the judges what is the position of the Argentine people."
The Supreme Court ruling -- adopted in a three-to-two vote by the court's justices -- upheld a law dating back two decades that allowed the shortening of offenders' sentences, with each day served in pre-trial detention counted as two days.
That calculation was applied earlier this month to the 13-year sentence of an ex-paramilitary fighter convicted in 2011 for crimes including torture and kidnapping.
But a court in the western city of San Juan on Tuesday refused to apply it in another case, calling it "unconstitutional and inapplicable."
The Supreme Court's decision opened the doors to a thousand people who have been convicted and another thousand being held pending outcomes of trials asking for early release.
Several inmates incarcerated for crimes committed during the dictatorship had already requested shortened sentences.
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