The Senate voted overwhelmingly on Tuesday night to give final approval to a $95.3 billion package of aid to Ukraine, Israel and Taiwan, sending it to President Biden and ending months of uncertainty about whether the United States would continue to back Kyiv in its fight against Russian aggression.

The vote reflected resounding bipartisan support for the measure, which passed the House on Saturday by lopsided margins after a tortured journey on Capitol Hill, where it was nearly derailed by right-wing resistance. The Senate’s action, on a vote of 79 to 18, provided a victory for the president, who had urged lawmakers to move quickly so he could sign it into law.

And it capped an extraordinary political saga that raised questions about whether the United States would continue to play a leading role in upholding the international order and projecting its values globally.

“Our allies around the world have been watching Congress for the last six months and wondering the same thing: When it matters most, will America summon the strength to come together, overcome the centrifugal pull of partisanship and meet the magnitude of the moment?” Senator Chuck Schumer, Democrat of New York and the majority leader, said on Tuesday. “Tonight, under the watchful eye of history, the Senate answers this question with a thunderous and resounding ‘yes.’”

In a statement minutes after the vote, Mr. Biden said he would sign the bill into law “and address the American people as soon as it reaches my desk tomorrow so we can begin sending weapons and equipment to Ukraine this week.”

“Congress has passed my legislation to strengthen our national security and send a message to the world about the power of American leadership: We stand resolutely for democracy and freedom, and against tyranny and oppression,” he said.

The House passed the package on Saturday in four pieces: a measure for each of the three U.S. allies and another meant to sweeten the deal for conservatives that includes a provision that could result in a nationwide ban on TikTok. It sent the legislation to the Senate as a single package that required only one up-or-down vote to pass.

Facing vehement opposition from his right flank to aiding Ukraine, Speaker Mike Johnson structured the legislation that way in the House to capture different coalitions of support without allowing opposition to any one element to defeat the whole thing. The majority of House Republicans opposed the aid for Kyiv.

The components of the bill are nearly identical to one that passed the Senate with bipartisan support in February. It includes $60.8 billion for Ukraine; $26.4 billion for Israel and humanitarian aid for civilians in conflict zones, including Gaza; and $8.1 billion for the Indo-Pacific region.

In addition to the package of sweeteners, which also includes new rounds of sanctions on Iranian and Russian officials, the House added provisions to direct the president to seek repayment from the Ukrainian government of $10 billion in economic assistance. That was a nod to a call by former President Donald J. Trump to make any further aid to Kyiv a loan. But the bill allows the president to forgive those loans starting in 2026.

Nine Republicans who opposed the Senate-passed aid legislation in February supported the bill this time. When Senator Markwayne Mullin of Oklahoma changed his vote on Tuesday, this time agreeing to advance the legislation, Senator Mitch McConnell, Republican of Kentucky and the minority leader, gave him a thumbs-up on the Senate floor.

“Seventy-five percent of the bill, the total funding, stays within the United States,” Mr. Mullin said on Newsmax, explaining his support for the bill. “That’s what a lot of people don’t realize. This goes to our defense industry; this goes to replenishing our munitions.”

Fifteen hard-right Republican senators who oppose aid to Ukraine voted against the legislation. Senator Tommy Tuberville of Alabama, who opposed the measure but was one of three Republicans who did not vote on final passage, argued that Congress was “rushing to further bankroll the waging of a war that has zero chance of a positive outcome.”

“Pouring more money into Ukraine’s coffers will only prolong the conflict and lead to more loss of life,” Mr. Tuberville said. “No one at the White House, Pentagon or State Department can articulate what victory looks like in this fight. They couldn’t when we sent the first tranche of aid over two years ago. We should be working with Ukraine and Russia to negotiate an end to this madness.”

Three liberals, Democratic Senators Jeff Merkley of Oregon and Peter Welch of Vermont, as well as Bernie Sanders, independent of Vermont, also opposed the measure. They said they could not endorse sending more offensive weapons to Israel when the government’s campaign in Gaza has killed tens of thousands of people and created a hunger crisis there.

“We are now in the absurd situation where Israel is using U.S. military assistance to block the delivery of U.S. humanitarian aid to Palestinians,” Mr. Sanders said. “If that is not crazy, I don’t know what is. But it is also a clear violation of U.S. law. Given that reality, we should not today even be having this debate. It is illegal to continue current military aid to Israel, let alone send another $9 billion with no strings attached.”

But the vast majority of senators in both parties supported the legislation, and Senate leaders regarded its passage as a triumph, particularly given the opposition to aid for Ukraine that had built up in the House.

For months, Mr. Johnson and right-wing Republicans in the House had refused to entertain aid to Ukraine unless Mr. Biden agreed to stringent measures to curtail immigration on the U.S. border with Mexico. When Senate Democrats agreed this year to legislation that paired the aid with stiffer border enforcement provisions, Mr. Trump denounced it and Republicans rejected it out of hand.

Then the Senate passed its own $95 billion emergency aid legislation for Ukraine, Israel and Taiwan without any immigration measures, ramping up political pressure on the House to do the same. For weeks, the message to Mr. Johnson from Mr. Schumer and Mr. McConnell had been the same: Pass the Senate bill.

In extensive remarks on the Senate floor on Tuesday before the procedural vote, Mr. McConnell cast congressional approval of the aid package as “a test of American resolve, our readiness and our willingness to lead.” He rebuked the naysayers in his party, criticizing those who, he said, would “indulge the fantasy of pulling up a drawbridge.”

“Make no mistake: Delay in providing Ukraine the weapons to defend itself has strained the prospects of defeating Russian aggression,” Mr. McConnell said. “Dithering and hesitation have compounded the challenges we face. Today’s action is overdue, but our work does not end here. Trust in American resolve is not rebuilt overnight. Expanding and restocking the arsenal of democracy doesn’t just happen by magic.”

Ukrainian officials cheered the impending passage of the bill.

Ruslan Stefanchuk, the speaker of the Ukrainian Parliament, posted a photograph on social media of lawmakers holding American flags inside the chamber in Kyiv, in “gratitude to the United States and to every member of the House of Representatives who supported the Ukraine Aid Bill. We look forward to a similar decision from the Senate.”

“The United States has been and remains a strategic partner that stands shoulder to shoulder with the Ukrainian people in our fight against the russian aggressor!” Mr. Stefanchuk added.

The photograph recalled the scene on the floor of the House on Saturday when Democrats waved miniature Ukrainian flags as they voted for the aid bill. They were rebuked by Mr. Johnson and other Republicans, who called it a violation of decorum and said that only American flags should be displayed in the chamber.

Lara Jakes contributed reporting from Rome.