The House voted 234-193 for the bill, a day after a Supreme Court ruling that broadly expanded gun rights.
No Democrats were opposed, while 14 Republicans backed the measure. It was supported by major law enforcement groups and its passage signalled a rare defeat for US gun manufacturers and the National Rifle Association.
The NRA, the nation's most powerful gun lobby, attacked the bill, calling it a "senseless" gun control measure that "will only infringe on the rights of the law-abiding".
House action followed a late Thursday Senate vote of 65-33 to pass the bill, with 15 Republicans, including Senate Minority Leader Mitch McConnell, in favour.
Gun laws have long been a divisive issue in the United States, with multiple attempts to place new controls on firearms sales failing time after time until Friday.
The bill does not go as far as Democrats, including Biden, had sought.
It includes provisions that would help states keep guns out of the hands of those deemed to be a danger to themselves or others, and close the so-called 'boyfriend loophole' by blocking gun sales to those convicted of abusing unmarried intimate partners.
However, it did not ban sales of assault-style rifles or high-capacity magazines.
"The legislation ... includes several strong steps to save lives, not only from horrific mass shootings but also from the daily massacre of gun crime, suicide and tragic accidents," House Speaker Nancy Pelosi said during debate.
The bill does take some steps on background checks by allowing access, for the first time, to information on significant crimes committed by juveniles.
It also cracks down on gun sales to purchasers convicted of domestic violence.
It provides new federal funding to states that administer 'red-flag' laws intended to remove guns from people deemed dangerous to themselves and others.
The Brady gun control group described the Bipartisan Safer Communities Act as "the strongest gun violence prevention law in the last 30 years", and cited the "100 people killed with guns each day" in America. Many of those deaths are the result of suicide.
The senior Republican on the House Judiciary Committee, Jim Jordan, was less happy with the outcome.
"Today they (Democrats) are coming after law-abiding American citizens' Second Amendment liberties," he said, referring to US constitutional right to "keep and bear arms" that conservatives argue should be broadly protected.
On Thursday, the Supreme Court, with its 6-3 conservative majority, struck down New York state's limits on carrying concealed handguns outside the home. The court found the law, enacted in 1913, was unconstitutional.
That ruling and the gun-safety legislation passed on Friday illustrate a deep divide over firearms in the United States, weeks after the Uvalde and Buffalo shootings that killed more than 30 people, including 19 young children at a primary school.
The NRA declared the court ruling "a monumental win" for American gun owners.
The legislation passed by Congress is seen as modest in scope for a country with the highest gun ownership per capita in the world and the highest number of mass shootings annually among wealthy nations.
In 2020, the rate of gun deaths in the United States surged 35 per cent to the highest point since 1994, with especially deadly levels for young Black men, the US Centers for Disease Control and Prevention said in a report published on May 10.
