In a statement, the White House said the two would discuss Ukraine's "urgent needs"
The meeting comes as the White House looks to strike an agreement with Congress that would provide military aid for Ukraine and Israel.
Zelenskiy's office said on the Telegram messaging app that the Ukrainian leader would arrive in Washington on Monday and he would meet Biden during a working visit that would include "a series of meetings and discussions."
Key topics during Zelenskiy's visit would include defence co-operation between the United States and Ukraine, "particularly through joint projects on the production of weapons and air defense systems, as well as the coordination of efforts between our countries in the coming year," Zelenskiy's office said.
Biden has asked Congress for a $US110 billion ($A167 billion) package of wartime funding for Ukraine ($US61.4 billion) and Israel, along with other national security priorities.
But the request is caught up in a debate over US immigration policy and border security.
Zelenskyy travelled to Buenos Aires to witness the swearing-in on Sunday of Argentina's new president, Javier Milei.
The Ukrainian leader had been scheduled to address US senators by video last week, but had to cancel the appearance, according to Senate Majority Leader Chuck Schumer of New York.
Biden's budget director, Shalanda Young, said in a letter this past week to House and Senate leaders that the US would run out of funding to send weapons and assistance to Ukraine by the end of the year, which would "kneecap" Ukraine on the battlefield.
"It's time to cut a deal that both sides can agree to," Young said on Sunday.
- with AP
