Trump tweeted Friday morning that he had signed the bill, writing that the USA military "will now be stronger than ever before".
The twin votes put to rest a brief federal freeze that relatively few would notice.
Wall Street's main stock indexes climbed more than 1 percent on Friday, giving investors some solace after a week of huge swings that shook the market out of months of calm.
The breakdown came largely in the Senate, when after a day of inaction, Republican Sen.
Paul voted for the deficit-financed tax bill in December.
Democrats, meanwhile, have qualms about the deal because it does not address the Deferred Action for Childhood Arrivals immigration program, which is set to end early next month.
Many Democrats support the budget deal, but were unhappy with the compromise because it doesn't tackle immigration - specifically addressing the plight of DREAMers, including the roughly 700,000 immigrants who are in the USA illegally after being brought to the country as children and who are enrolled in the Deferred Action for Childhood Arrivals (DACA) program, which is set to expire on March 5.
As of late Thursday, it was not clear whether there would be enough Republican votes to pass the bill in the House, meaning most likely some Democrats would have to vote for it to reach a simple majority, a fact House Speaker Paul Ryan alluded to in a Thursday morning radio interview with Hugh Hewitt.
Despite the delays, the Senate is due to vote on the budgetary measure after 01:00.
At the White House, there appeared to be little sense of concern. Trump did not tweet on the issue Thursday and aides did not try to assign blame. Even some of Paul's fellow fiscal conservatives, like Sen.
Tea Party Patriots Chair Jenny Beth Martin warned that if Republicans could not keep their promise to rein in federal spending, "perhaps it's time for a new Congress". But Paul, the resident contrarian, repelled suggestions to stand aside.
"I didn't come up here to be part of somebody's club. This is not what the American people sent us here to do", the 30 or so members of the group said on Wednesday.
No. 2 Senate Democratic leader Richard Durbin of IL, a leader in the immigration fight, said the budget pact "opens the door" for Senate votes on protecting the young immigrants.
That won over many Republicans, but some were furious over the $131 billion extra made available for non-military spending, including health and infrastructure.
McDonald to be ratified as new leader of Sinn Féin
There is now a peaceful and democratic path to Irish unity, a way to unite Orange and Green and end division. He told PA he regretted the blood spilt during Northern Ireland's three-decade Troubles.
The agreement would increase the government's borrowing limit to prevent a first-ever default on USA obligations that looms in just a few weeks. It raises the federal debt limit until March 2019 and adds $90 billion in disaster relief.
Senate leaders had celebrated the budget deal as a sign they had left behind some of their chronic dysfunction.
In January, a similar failure to pass a bill led to a three-day government shutdown.
Senate Democrats had no appetite for another shutdown.
However, House GOP leaders were confident they had shored up support among conservatives for the measure, which would shower the Pentagon with money but add hundreds of billions of dollars to the nation's $20 trillion-plus debt.
House Democratic leaders opposed the measure - arguing it should resolve the plight of Dreamers - but not with all their might.
"Democrats have fought hard but, in the end, many opted to say yes to other priorities and leave Dreamers behind", said Frank Sharry, executive director of the pro-immigration America's Voice.
"She negotiated the deal". Thom Tillis, R-N.C., said on the Senate floor.
"There's a lot of no votes in there", said California Rep. Pete Aguilar after the meeting.
Democrats have their own problems with the measure.
House Speaker Paul Ryan, R-Wis., pledged on the House floor early Friday morning that he also meant to address immigration. It also includes $89 billion for disaster relief sought by both parties. "We will bring a solution to the floor, one that the president will sign".
Republicans, too, had their disappointments.
Republicans were sheepish about the bushels of dollars for Democratic priorities and the return next year of one trillion dollar-plus deficits.
These provisions had been opposed by fiscal conservatives in the Republican party who objected to the deficit spending it would bring in.
"It provides what the Pentagon needs to restore our military's edge for years to come, " said Ryan. There's also $16 billion to renew a slew of expired tax breaks that Congress seems unable to kill. Asked if McConnell was annoyed with him, Paul said: "Not that I know of".
While the USA government's authority to spend some money would expire at midnight, there were not likely to be many clear immediate effects.