Pat Toomey, a Pennsylvania Republican, and Joe Manchin, a West Virginia Democrat, told reporters on Capitol Hill the expanded background checks would apply to all sales at gun shows and online, and would require records be kept to document background checks were carried out.
The agreement exempts sales and transfers of firearms conducted between friends and acquaintances, The Hill reported. It prohibits the establishment of a federal government firearms registry.
Toomey said in announcing the agreement he doesn't consider criminal background checks to be gun control, just "common sense."
"If you pass a criminal background check, you get to buy a gun," he said. "It's not a problem. It's the people who fail a criminal or mental health background check that we don't want having guns."
Background checks under the compromise would be stricter than under current law, which requires checks when purchases are made through a licensed dealer, but less stringent than the universal background checks sought by President Barack Obama and congressional Democrats after the Dec. 14 massacre at Sandy Hook Elementary School in Newtown, Conn., in which 20 school children and six staffers were killed.
"The events at Newtown, surely the events at Newtown, changed us all," Manchin said Wednesday.
Obama praised Manchin and Toomey "for their leadership on forging a bipartisan agreement around commonsense background checks that will make it harder for dangerous people to get their hands on a gun."
In a statement issued by the White House, the president said "there are aspects of the agreement that I might prefer to be stronger" but he said the compromise "does represent welcome and significant bipartisan progress."
"It recognizes that there are good people on both sides of this issue, and we don't have to agree on everything to know that we've got to do something to stem the tide of gun violence," he said.
Obama said Congress "needs to finish the job."
"The Senate must overcome obstruction by defeating a threatened filibuster, and allow a vote on this and other commonsense reforms to protect our kids and our communities," the president said. "Any bill still has to clear the House. So I'm going to keep asking the American people to stand up and raise their voices, because these measures deserve a vote -- and so do the families and communities they're designed to protect."
Senate Majority Leader Harry Reid, D-Nev., has said the bipartisan proposal would be the first issue considered once formal debate on his gun bill begins Thursday.
NBC News said Toomey and Manchin reached an agreement in principle Tuesday evening and spent the night working out the final details. Among other things, the compromise would exempt some transactions, such as those within a family, from background checks.
The NRA issued a statement critical of the Senate compromise.
"Expanding background checks at gun shows will not prevent the next shooting, will not solve violent crime and will not keep our kids safe in schools," the NRA said. "While the overwhelming rejection of President Obama and [New York] Mayor [Michael] Bloomberg's 'universal' background check agenda is a positive development, we have a broken mental health system that is not going to be fixed with more background checks at gun shows. The sad truth is that no background check would have prevented the tragedies in Newtown, Aurora or Tucson."
The NRA called instead for "a serious and meaningful solution that addresses crime in cities like Chicago, addresses mental health deficiencies, while at the same time protecting the rights of those of us who are not a danger to anyone. President Obama should be as committed to dealing with the gang problem that is tormenting honest people in his hometown as he is to blaming law-abiding gun owners for the acts of psychopathic murderers."
The deal represents a huge breakthrough for a package of new anti-gun-violence laws Obama proposed following the shooting in Newtown.
Republican Sens. Kelly Ayotte of New Hampshire, Saxby Chambliss of Georgia, Tom Coburn of Oklahoma, Susan Collins of Maine, Lindsey Graham of South Carolina, Dean Heller of Nevada, Johnny Isakson of Georgia and Kirk have indicated they will join Democrats in opposing a threatened filibuster by Tea Party-backed GOP Sens. Rand Paul of Kentucky, Mike Lee of Utah and Ted Cruz of Texas, intended to block Senate consideration of gun-control legislation, aides said.
"It's incomprehensible to me that we would not move forward with debate and amendments on an issue this important to the American people," said Sen. John McCain, R-Ariz.
Collins is co-sponsoring the bill's gun-trafficking and school-safety provisions.
With backers of new gun-safety laws increasingly optimistic they will have the 60 votes needed to overcome the filibuster and bring the bill to the floor, Reid said he would schedule a showdown vote for Thursday.
"We're moving forward on this bill," Reid said.
Reid earlier invoked his father's suicide by gunshot to appeal for consideration of the legislation, which would also crack down on people who purchase firearms for those who are not permitted to own them.
"The American people deserve a vote on this legislation," Reid said.