In a trip showing solidarity with Kyiv, Biden also said additional sanctions would be announced this week against the Russian elite and companies trying to evade sanctions to support Russia.
The military aid package will include artillery ammunition, anti-armour systems, and air surveillance radars.
Biden appeared to make no mention of fighter jets, which Ukraine has been seeking from Western allies to help it push back the Russian forces.
A year ago, Biden warned sceptical allies that a massive buildup of Russian troops along Ukraine's borders was the precursor to war. At the time, even some inside his own government questioned the ability of the Ukrainians to withstand an invasion, predicting the imminent fall of the capital Kyiv.
Instead, Ukrainian fighters have held the capital and continue to resist Russian attempts to control territory, helped by a massive influx of Western weapons, ammunition, and equipment.
The war has become a grinding conflict that US officials say could last for months or even years.
White House press secretary Karine Jean-Pierre said Biden intends to send "a strong message of solidarity" during his Feb 20-22 trip. Senior White House officials have said Biden will emphasize the importance of unity in the uncertain months ahead. His message will make clear the US will stand with Ukraine for "as long as it takes," White House spokesperson John Kirby told reporters. The United States, he said, is right now focused on making sure Ukraine has the tools to succeed on the battlefield.
Since the start of the war, the US has sent over $24 billion in security assistance to help Kyiv. In January, the US said it will supply Ukraine with 31 advanced M1 Abrams tanks worth $400 million in a matter of months.
Offering similar support and keeping the war from escalating into a potentially wider conflict with Nato will be one of Biden's key foreign policy tests in the months to come, experts said.
Earlier in February, 11 House Republicans introduced the "Ukraine fatigue" resolution urging Biden to end military and financial aid to Ukraine while pushing Ukraine and Russia to come to a peace agreement Michal Baranowski, a managing director with the German Marshall Fund East, said there is a concern, both in Poland and in Ukraine, about the staying power of the United States beyond this administration.
Biden landed in the Polish capital Warsaw on Monday evening and is scheduled to meet with Polish President Andrzej Duda before delivering remarks on Tuesday evening Polish time.
On Wednesday, Biden will meet with the Bucharest Nine, which consists of members of Nato's eastern flank: Poland, Romania, Slovakia, Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, and Lithuania.
On Saturday (February 18), Vice President Kamala Harris said at the Munich Security Conference that the US has formally concluded that Russia has committed "crimes against humanity" during its invasion of Ukraine.
In December, Biden welcomed Ukrainian leader Volodymyr Zelenskiy to the White House with renewed assurances of American support for Ukraine's defence against a Russian onslaught.