The vote gave President Bill Clinton a sorely needed victory.
Clinton said he was "very grateful" to the Republicans who helped negotiate the package with Democrats after the House shelved an earlier, $33.5 billion version on Aug. 11.
The vote was 235-195 for the new package, completed before dawn Sunday. It survived two votes that could have stopped it in its tracks.
"This is the way Washington should work, and I hope it works this way in the future," Clinton said of the bipartisan effort.
Of the 235 votes in favor, 188 were Democrats, 46 were Republicans and one was independent. Voting against it were 131 Republicans and 64 Democrats.
Clinton recognized that "this fight is far from over," since conservative Republicans in the Senate have vowed to stall action because of crime-prevention spending in the bill that they have criticized as "pork."
Nonetheless, the House vote was a victory for Clinton and for the moderate Republicans, most of whom supported the firearms ban, who worked with Democratic leaders to work out the new bill after Democratic gun-control opponents deserted Clinton.
The president lobbied strenuously for the bill and dispatched several top Cabinet officials to Capitol Hill to lobby in person Sunday.
Earlier, the House had voted 197-232 to turn aside a motion to send the measure back to a House-Senate conference to be reformulated like the alternative authored by two gun-control opponents.
Still earlier, it had voted 239-189 for a procedural motion that moved the crime bill to the House floor for consideration just 10 days after it defeated a similar move that prevented consideration of the $33.5 billion version.
Despite a surge of support for the alternative, majority leader Richared Gephardt predicted hours before the final series of votes that the House would approve the compromise worked out at 3 A.M. Sunday.
The compromise agreed to by negotiators would authorize spending $10.8 billion on state and local law enforcement, including $8.8 billion to help put 100,000 new police on the streets. It also would authorize $2.6 billion for federal law enforcement, $9.85 billion for prisons and $6.9 billion for crime prevention.
It would allow lifetime imprisonment for some three-time violent and drug felons, expand the death penalty to more than 50 additional crimes and allow 13-year-olds to be tried as adults for many violent federal crimes.
House Judiciary Committee Chairman Jack Brooks, despite his opposition to the firearms ban, told the House: "It's important that we move forward today with the legislation, no longer defer our compact with the people to ensure their safety and productivity."
On the other side, Representative Bill McCollum called the legislation, "a very bad bill," saying it does not "put swiftness and certainty of justice back into the American justice system."
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