But his most crucial date is likely to be with leaders of the Republican and Democratic parties from the US Congress, where a new multibillion-dollar aid package for Kyiv is at risk of being blocked.
The White House said the Ukrainian leader's visit came at a "really critical time" as Ukraine's slow-moving counteroffensive against Russian forces grinds forward into fall.
Zelensky will arrive fresh from the United Nations General Assembly in New York, where he urged the world to stand firm with Ukraine against Russia's "genocide."
He asked Americans to keep up their support which has seen Washington pump more than $43 billion in military aid to Ukraine since Russia's February 2022 invasion.
"We are on the finishing line," he told CNN on Tuesday.
- 'Brutalize Ukraine' -
But Zelensky's trip to Washington will be very different from his first wartime visit in December 2022, when he secretly flew in and received a hero's welcome at the White House and on Capitol Hill.
This time doubts are growing over the future of US assistance, with hardline Republicans saying they won't approve funding to prevent a US government shutdown if it includes aid for Ukraine.
Biden has pledged to stand by Kyiv no matter what -- not least as his 2024 reelection campaign portrays his support for Ukraine as demonstrating his global leadership.
The US president and First Lady Jill Biden will greet Zelensky and his wife Olena Zelenska at the White House, before the two leaders have head-to-head talks in the Oval Office, according to US officials.
Biden is "looking forward to getting a battlefield perspective directly from Ukraine's commander in chief," National Security Council spokesman John Kirby said.
Zelensky's reported request for longer-range ATACMS missiles that can strike up to 300 kilometers (190 miles) away is "not off the table" but there has been no decision yet, Kirby added.
"The president will be talking to President Zelensky about his needs and about how the United States will continue to meet those needs."
Biden, speaking Tuesday at the UN, warned against abandoning Ukraine, saying that "Russia believes that the world will grow weary and allow it to brutalize Ukraine without consequence."
His warning came a day before Poland said it would no longer arm Ukraine in a mounting row over grain exports.
- 'What's the plan?' -
Zelensky also faces the delicate task of wooing Congress, where Ukraine's hopes are hostage to the drama over a looming government shutdown.
Hard-right Republican lawmakers are holding up the White House's demand for any budget bill passed by Congress to include a further $24 billion in military and humanitarian aid for Kyiv.
But even more moderate Republicans have their doubts.
"What's the plan for victory? I think that's what the American public wants to know," Republican House Speaker Kevin McCarthy said this week.
Some say the money could be better spent on US border security, while there are also concerns about the pace of Kyiv's counteroffensive and that corruption in Ukraine means the money will go to waste.
Former president Donald Trump, the frontrunner to challenge Biden next year, has said the money would be better spent at home and predicted an eventual triumph for Russian President Vladimir Putin, for whom he has shown admiration.
