The relief measure would deliver money to Southern states suffering from last fall's hurricanes, Midwestern states deluged with springtime floods and fire-ravaged rural California, among others. Puerto Rico would also get help for hurricane recovery.
The Senate approved the bill by an 85-8 vote. House lawmakers have left for the Memorial Day recess, but the chamber probably will try to pass the bill by voice vote Friday, said a spokesman for House Speaker Nancy Pelosi, D-Calif.
Trump said he will sign it even though money to deal with the border has been removed.
"I didn't want to hold that up any longer," Trump said. "I totally support it."
Much of the money would go to Trump strongholds such as the Florida Panhandle, rural Georgia and North Carolina, and Iowa and Nebraska. Several military facilities would receive money to rebuild, including Camp Lejeune in North Carolina and Offutt Air Force Base in Nebraska.
Disaster aid bills are invariably bipartisan, but this round bogged down.
After weeks of fighting, Democrats bested Trump and won further aid to Puerto Rico, the U.S. territory slammed by back-to-back hurricanes in 2017. Trump has feuded with the island's Democratic officials and has repeatedly misstated that Puerto Rico has received much more aid than it actually has.
Trump originally wanted no money for Puerto Rico before agreeing to $605 million for its food stamp program. But ultimately, Democrats said they secured about $1.4 billion, including money to help Puerto Rico's cash-poor government meet matching requirements for further disaster rebuilding efforts.
Talks this week over Trump's border request broke down, however, over conditions Democrats wanted to place on money to provide care and shelter for asylum-seeking Central American migrants. Talks were closely held, but aides said liberal and Hispanic forces among House Democrats could not come to terms with administration demands.
Senate Democratic leader Chuck Schumer of New York dictated the terms of the agreement because Senate Majority Leader Mitch McConnell, R-Ky., was in a procedural box. Schumer took a victory lap with reporters immediately after the vote, recounting how he bested Trump on money for Puerto Rico and then carried the day by forcing a vote on the natural disaster-only measure.
Schumer said the bill was virtually the same as what he and Vermont Sen. Patrick Leahy, the top Democrat on the Senate Appropriations Committee, proposed six weeks ago. He said the bill "could have been passed then. It wasn't Democrats blocking it."
Schumer led a filibuster of an earlier version last month over Trump's refusal to sign off on money to speed further disaster aid to Puerto Rico.
He said Democrats "insisted that Puerto Rico get the aid that it needed, along with the rest of America, and it is."
"This funding will replenish Puerto Rico's nutrition assistance program, fund important disaster recovery projects, and allow critical infrastructure like hospitals and schools to be built back better," said House Appropriations Committee Chairwoman Nita Lowey, D-N.Y.
But border needs are increasingly desperate, and lawmakers will face intense pressure to act when they return next month. Money to house and care for migrants is expected to run out in June.
The disaster aid bill was most urgently sought by southern Republicans such as Sen. David Perdue of Georgia, who want to help farmers who lost billions of dollars when Hurricane Michael hit last fall during harvest season. Midwestern Republicans such as Sen. Joni Ernst of Iowa also pressed for the legislation.
Democrats didn't pay a political price for filibustering the bill in early April, and Schumer remained confident that Republicans such as Perdue - who is close to Trump and faces reelection next year - were getting desperate. Pressure built, and Trump agreed to sign the measure after a phone call with Perdue and the chairman of the Senate Appropriations Committee, Sen. Richard Shelby, R-Ala.
All sides agree that another bill of more than $4 billion will be needed almost immediately to refill nearly empty agency accounts to care for migrants, though Democrats are fighting hard against the detention facilities requested by Trump.
Part of the rush to get the bill through without the refugee aid was to get politically exhausted lawmakers out of Washington, but Republicans controlling the Senate were determined to get disaster aid completed or face the wrath of frustrated constituents.
"Right now the total dollar amounts are pretty close on border security. Democrats and Republicans are pretty much in agreement about it," said Perdue. "We're just trying to work out some detailed language, but we didn't think we could wait any longer to get this done."
Trump rushed to try to claim credit, too, though his budget office never submitted an official request for the disaster aid. But he talked up the aid in a recent trip to the timber-rich Florida Panhandle, his best region in a state without which it's virtually impossible for him to win reelection.
"Well, we're going to get the immigration money later, according to everybody," Trump said. "I have to take care of my farmers with the disaster relief."
Democrats secured a provision that would block Trump from diverting any of the money in the bill for military projects toward building his border wall. Trump has declared a national emergency and has said he is considering transferring up to $3.6 billion from military construction to border barriers.
The measure also includes a temporary extension through September of the government's troubled flood insurance program, which is critical to the housing market in coastal and flood-prone areas.
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