The Senate could vote as soon as Wednesday.
The package was expected to pass the chamber Wednesday and head to the House of Representatives and eventually President Donald Trump's desk.
"The arrows are headed in the right direction", Cuomo told reporters.
It will give $500 billion in direct payments to the American public, bolster unemployment insurance with a surge of $250 billion, provide $500 billion in loans to big businesses, and creates a $350 billion loan program for small businesses.
Treasury Secretary Steven Mnuchin has been meeting with Senate Minority Leader Chuck Schumer to resolve Democrats' complaints about the Republican legislation.
The United States has the third-highest number of infections globally behind China and Italy.
But it was delayed by criticism from both the right and left on Wednesday, pushing the final vote on passage nearly another full day.
After weeks of negotiations, the deal thrashed out between Republicans, Democrats and the White House includes cash payments to American taxpayers; several hundred billion dollars in grants and loans to small businesses and core industries; medical equipment to hospitals and unemployment benefits.More news: Coronavirus: Italian priest dies after conceding respirator to younger patient
The Senate cleared these measures by an overwhelming majority.
There had been criticism of the bill from the most progressive wing of the Democratic-led House.
Ardent liberals like Rep. Alexandria Ocasio-Cortez were restless as well, but top Washington Democrats assured them that additional coronavirus legislation will follow this spring and signaled that delaying the pending measure would be foolish.
It wasn't easy, and it took a little longer than many would've liked, but around 2 a.m. (E.T.) this morning, Senate leaders and the White House reached an agreement on a $2 trillion economic rescue bill, meant to help mitigate the effects of the coronavirus crisis. Bringing more than 400 lawmakers from as far away as Hawaii and Alaska would be hard because a few are in self-quarantine and several states have issued stay-at-home orders.
House Speaker Nancy Pelosi, D-Calif., praised the Senate bill Wednesday night after lambasting an earlier version of the legislation.
A birthday party is believed to have spurred a super-spreading event as there were attendees who went back home to NY, the hardest-hit state in the U.S. Workers building a makeshift morgue outside of Bellevue Hospital in NY.
Other objections floated in from New York Gov. Andrew Cuomo, who has become a prominent Democrat on the national scene as the country battles the pandemic.
Pelosi said she was sympathetic to Cuomo and other state officials, but wanted a rescue package to move on. "We (Congress) do have to do more, but that would be no reason to stop this step that we are taking", she told CNN.More news: National Hockey League postpones 2020 draft amid coronavirus pandemic
Underscoring the effort's sheer magnitude, the bill finances a response with a price tag that equals half the size of the entire $4 trillion-plus annual federal budget.
Investors were cheered by the news or the deal. On Wall Street, the benchmark S&P 500 rallied for a second straight day, closing up 1.15 per cent.
McConnell also announced that, after passing the bill, the Senate would leave Washington and be in recess at least until April 20.
Tempers flared on Monday on Capitol Hill as senators grappled with the need to pass the critical aid.
Missing from Wednesday's votes was No. 2 Senate Republican John Thune, who said in a statement he did not feel well when he woke up on Wednesday and made a decision to take a charter flight home to South Dakota "out of an abundance of caution".
Thune did not say whether he had coronavirus symptoms, although he said he was not advised to self-quarantine. Two members of the House and one senator have recently tested positive for the coronavirus illness COVID-19.
The just-agreed coronavirus emergency aid bill is set to become the largest by far in American history.More news: Kanika Kapoor tests positive in her third COVID-19 test