"I am grateful to the President of the United States for the invitation. We all equally want to end this war swiftly and reliably," Zelenskiy said on X after arriving in Washington late on Sunday.
"And I hope that our shared strength with America and with our European friends will compel Russia to real peace."
Trump's bilateral meeting with Zelenskiy will take place on Monday at 1:15pm (3:15am AEST Tuesday), the White House said in a statement.
Trump will participate in a multilateral meeting with European leaders visiting Washington at 3pm local time.
Trump is publicly pushing Zelenskiy to come to a negotiated settlement in the three-and-a-half-year-old conflict with Russia.
"President Zelenskyy of Ukraine can end the war with Russia almost immediately, if he wants to, or he can continue to fight," Trump said on his Truth Social platform and seemed to indicate that reclaiming Crimea and joining NATO are off the table for Ukraine.
"No getting back Obama given Crimea...and NO GOING INTO NATO BY UKRAINE. Some things never change!!!"
European leaders are seeking to shore up Zelenskiy's position as the US president presses Ukraine to accept a quick peace deal to end Europe's deadliest war in 80 years.
Trump is leaning on Zelenskiy to strike an agreement after he met Russian President Vladimir Putin in Alaska last week and emerged more aligned with Moscow on seeking a peace deal instead of a ceasefire first.
Sources briefed on Moscow's thinking told Reuters the US and Russian leaders have discussed proposals for Russia to relinquish tiny pockets of occupied Ukraine in exchange for Kyiv ceding a swathe of fortified land in the east and freezing the front lines elsewhere.
Top Trump officials hinted that the fate of Ukraine's eastern Donbas region - which is already mostly under Russian control - was on the line, while some sort of defensive pact was also on the table.
"We were able to win the following concession, that the United States could offer Article 5-like protection," Trump envoy Steve Witkoff told CNN's State of the Union on Sunday, suggesting this would be in lieu of Ukraine seeking NATO membership.
He said it was "the first time we had ever heard the Russians agree to that".
Article 5 of NATO's founding treaty enshrines the principle of collective defence, in which an attack on any member is considered an attack on all.
That pledge may not be enough to sway Kyiv to sign over Donbas.
German Chancellor Friedrich Merz, French President Emmanuel Macron, and British Prime Minister Keir Starmer hosted a meeting of allies on Sunday to bolster Zelenskiy's hand, hoping in particular to lock down robust security guarantees for Ukraine that would include a US role.
The Europeans are eager to help Zelenskiy avoid a repeat of his last Oval Office meeting in February when Trump and Vice President JD Vance gave the Ukrainian leader a public dressing-down, accusing him of being ungrateful and disrespectful.
European Commission President Ursula von der Leyen will also travel to Washington, as will Finnish President Alexander Stubb, who has played rounds of golf with Trump this year, and Italian Prime Minister Giorgia Meloni, an admirer of many Trump policies.
A joint communique released by Britain, France and Germany after the meeting said their leaders were ready "to deploy a reassurance force once hostilities have ceased, and to help secure Ukraine's skies and seas and regenerate Ukraine's armed forces".
Zelenskiy said on X there had been "clear support for Ukraine's independence and sovereignty" at the meeting. "Everyone agrees that borders must not be changed by force".
Any prospective security guarantees "must really be very practical, delivering protection on land, in the air, and at sea, and must be developed with Europe's participation".
Rubio said both Russia and Ukraine would need to make concessions to reach a peace deal.
