Senators approved the bill late Monday, December 21, hours after it was passed by the House of Representatives.
The new financial aid includes direct payments for many Americans and support for businesses and unemployment programmes.
The money is to accompany a bigger, $1.4tn spending bill to fund government operations over the next nine months.
The stimulus includes one-off $600 payments to most Americans, and will boost unemployment payments by $300 per week, extending expiration dates for the jobless programmes until the spring.
It also contains more than $300bn in support for businesses, and money for vaccine distribution, schools and tenants facing eviction.
US President Donald Trump has no problems with the deal and is expected to sign the package into law, according to reports.
In the House, the bill passed by a vote of 359 to 53 and in the Senate it passed by 92-6.
Many Covid-19 relief programmes were set to expire at the end of the month and about 12 million Americans were at risk of losing access to unemployment benefits.
But some lawmakers said they felt blind-sided by being asked to vote on a mammoth bill without even having a chance to read it.
At nearly 5,600 pages, the legislation was described by the Associated Press news agency as “the longest bill in memory and probably ever”.
The package also includes an extension of an eviction moratorium that was due to expire at the end of this month, leaving tens of millions of Americans at risk of being thrown out of their homes.
The bill also has a provision to end surprise medical billing – where hospital patients get slapped with fees because they were treated by a doctor who was not covered by their health insurer.
The deal was announced by Senate Majority Leader Mitch McConnell, a Republican. “We can finally report what our nation has needed to hear for a very long time: More help is on the way,” he said.
House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer, both Democrats, said the package delivered “urgently needed funds to save the lives and livelihoods of the American people as the virus accelerates”.
The first cheques could arrive as soon as next week, Treasury Secretary Steven Mnuchin said.Mr Schumer said the package would “establish a floor, not a ceiling, for coronavirus relief in 2021”, and that Democrats would push for more aid after President-elect Joe Biden took office on 20 January.