The aid measure passed by the Democratic-controlled house, part of a $US1.66 ($A2.48) trillion government funding bill that won Senate approval a day earlier, will now go to US President Joe Biden for signing into law.
In a tweet thanking Congress and leaders of both parties, Zelenskiy said it was "crucial" that Americans are "side-by-side" with Ukrainians "in this struggle".
The new military and economic assistance would come atop some $US50 billion ($A75 billion) in aid to Ukraine this year as well as Western sanctions on Russia that now include a cap on Russian oil prices.
Russia responded to the cap on Friday by threatening to cut oil output by five to seven per cent early next year by halting sales to countries that support the measure.
Zelenskiy returned from Washington - his first trip outside of Ukraine since Russia invaded on February 24 - with the pledge by the US of a Patriot surface-to-air missile battery to bolster his hard-pressed air defences.
He long has sought Patriot missiles to help counter three months of Russian missile and drone strikes on civilian infrastructure, including Ukraine's power grid.
Millions have been left without electricity, heat and water as temperatures plunge below freezing.
US officials say, however, that the single Patriot battery that Biden promised Zelenskiy during their White House meeting on Wednesday will not change the course of the war.
In his regular nightly video address, Zelenskiy warned Ukrainians that Russia could launch more strikes over Christmas, urging them to "pay attention to air raid alarms, help one another and look out for one another".
"With the holiday season fast approaching, the Russian terrorists could again step up their activities," he said.
"They have no regard for Christian values or any values for that matter."
Switching to Russian, Zelenskiy warned that "citizens of Russia must clearly understand that terror never goes without a response".
He did not elaborate.
He said that he had met his top commanders to review the military situation and that his government is "preparing for various scenarios of action by the terrorist state".
"And we will respond," he said.
Washington and its allies have been unwilling to supply Kyiv with modern battle tanks and long-range missiles called ATACMS that could reach far behind the frontlines and into Russia itself.
Kyiv and the Biden administration are wary that retaining US congressional support for aid could become more complicated when Republicans take a slim majority in the House next year - some right-wing Republicans oppose aid and other lawmakers have called for tighter oversight.
Russian President Vladimir Putin made a visit on Friday to the city of Tula, known for arms manufacturing, where he was shown telling defence industry chiefs to boost the output of weapons for the front.
In Bakhmut, an eastern Ukrainian city that has become the target of Russian attempts to advance in recent weeks in fighting that has killed thousands of soldiers, Valerii Deriukha, 55, was one of the few residents who have not fled.
He was chopping twigs for firewood as artillery explosions rang out.
"You see with your own eyes what life is like here. What life? It is war," he said.
Two storeys had been blasted off a building nearby.
"How is life? You see for yourself."
Russian forces shelled the southern Kherson region 61 times in 24 hours, half of those within Kherson city, killing one person, Governor Yaroslav Yanushevych said.
Russia withdrew from that city last month.
Reuters was not able to confirm the battlefield reports.
