Live updates: follow the latest news on Russia-Ukraine
“We look forward to the privilege of welcoming President Zelenskyy's address to the House and Senate and to convey our support to the people of Ukraine as they bravely defend democracy,” House Speaker Nancy Pelosi and Senate Majority Leader Chuck Schumer said in a joint letter to Congress on Monday.
“The Congress remains unwavering in our commitment to supporting Ukraine as they face [Russian President Vladimir] Putin's cruel and diabolical aggression and to passing legislation to cripple and isolate the Russian economy as well as deliver humanitarian, security and economic assistance to Ukraine.”
The Democratic leaders said Mr Zelenskyy's address would begin at 9am.
Mr Zelenskyy will likely get a more receptive audience than his predecessor Petro Poroshenko did several months after Russia annexed Crimea in 2014.
Republicans at the time demanded former president Barack Obama's administration do more to aid Ukraine to reclaim Crimea, but the White House resisted those calls out of fear of provoking Russia.
“One cannot win the war with blankets. One cannot keep the peace with blankets,” Mr Poroshenko said at the time, as then-vice president Joe Biden sat behind him in the House chamber.
Mr Zelenskyy will be addressing a Congress that is much more unified on Ukraine, having already sent an aid package to Mr Biden's desk to sign that will provide the country with weapons and other equipment.
But the Ukrainian president won't get all of his asks. The US, as well as other Nato members, have thus far refused to implement a no-fly zone over his country. A direct confrontation between Nato and Russia "is World War III", Mr Biden argued.
Still, Congress is expected to move quickly this week to end normal trade relations with Moscow after Mr Biden announced the intention to revoke Russia's preferred trade status.
The House of Representatives will “take up legislation to formalise this revocation and it is our hope that it will receive a strong, bipartisan vote”, Ms Pelosi said in a press release.
Stripping Russia of its “most favoured nation” trade status requires an act of Congress, but the White House is expected to co-ordinate with the legislative body on the action. Mr Biden lauded both Democratic and Republican leaders for supporting the move.
Mr Zelenskyy thanked Mr Biden for moving to revoke the status in a phone call last week but pressed the US president to apply even more pressure to isolate Russia from international trade, CNN reported.
The US on Saturday announced it would send an additional $200 million in weapons assistance to Ukraine.
Mr Zelenskyy will also address Canada's Parliament via video on Tuesday, Prime Minister Justin Trudeau announced last week while in Germany for a meeting with Chancellor Olaf Scholz.
The Ukrainian president pressed the UK Parliament last week for additional sanctions and more arms during an address to the House of Commons.
Agencies contributed to this report