"It's going to make America safer, it's going to make the world safer," he said after signing the bill into law.
The president said the US would "right away" send fresh weapons and equipment to Ukraine to help Kyiv fend off Russian advances.
Comment: The West has depleted much of its weapon stocks, so much of the money is to go to US weapons manufacturers to actually make the weapons, first.
He spoke a day after the US Senate approved the aid package following months of congressional gridlock.
Comment: Footage:
Ukraine has recently stepped up its calls for Western assistance as Russia makes steady gains in its invasion.
Included in the package is $61bn in military aid for Ukraine. It passed the Senate in a bipartisan vote of 79-18.
Tuesday evening's approval came after the measure passed the US House of Representatives on Saturday.
Democratic Senate Majority Leader Chuck Schumer said: "After more than six months of hard work and many twists and turns in the road, America sends a message to the entire world: we will not turn our back on you."
Comment: They will, however, turn their backs on their own citizens.
Reacting to the vote, Ukrainian President Volodymyr Zelensky said it "reinforces America's role as a beacon of democracy and leader of the free world".
The Senate passed a similar aid package in February, but a group of conservatives who oppose new Ukraine support had prevented it from coming to a vote in the House of Representatives.
Last week, Democrats and Republicans in the lower chamber joined together to bypass this opposition.
They ultimately agreed to a package bill that included the foreign aid as well as legislation to confiscate Russian assets held by Western banks; new sanctions on Russia, Iran and China; and a provision that will force the Chinese company ByteDance to sell the popular social media service TikTok.
Comment: The theft of Russian assets will backfire, both with Russia's retaliation, and global investors who will be reluctant to operate in the US; as will the sanctions; and the control of TikTok only further serves as proof of America as a surveillance state.
In the House on Saturday, a majority of Republicans in the chamber voted against the foreign aid package.
The bill also faced resistance among a handful of Senate Republicans who opposed any new aid to Ukraine.
Fifteen voted with two Democrats - as well as independent Senator Bernie Sanders who objected to providing new offensive weapons to Israel - against the bill.
"Pouring more money into Ukraine's coffers will only prolong the conflict and lead to more loss of life," Republican Senator Tommy Tuberville said in remarks on Tuesday.
"No-one at the White House, the Pentagon, or the state department can articulate what victory looks like in this fight."
The aid package is expected to provide a significant boost to Ukraine's forces, which have suffered from a shortage of ammunition and air defence systems in recent months.
On Tuesday, Ukraine's second city, Kharkiv, faced the latest in a series of recent drone and missile strikes, with authorities saying two people in a residential neighbourhood were injured.
The commander of Ukraine's National Guard, Oleksandr Pivnenko, said he was expecting an attempt by Russian forces to advance on the city, which is near the Russian border.
Between February 2022 and January 2024, the US gave Ukraine more than $40bn in military aid, according to German research organisation, the Kiel Institute.
Comment: The EU has allocated 50 Billion euros of taxpayers money.
Aid for Israel and Taiwan
The foreign aid package passed on Tuesday also allocates $17bn to Israel, as well as $9bn for civilians suffering in conflict zones around the world, including Palestinians in Gaza.
Comment: So $17 billion to wage genocide, less than a few billion for those suffering from it?
A further $8bn has been earmarked for allies in the Asia-Pacific, including Taiwan, to "counter communist China".
Comment: Countering them by threatening them on their border: US army stations special forces 'permanently' near mainland China's coast, begins training Taiwan's troops
Israeli Foreign Minister Israel Katz reacted to the vote by thanking congressional leaders for their "unwavering commitment to Israel's security".
"Israel and the United States stand together in the fight against terrorism, defending democracy and our shared values," he said.
The US already provides Israel with $3.8bn in military aid each year.
Over in Asia, a Chinese government spokeswoman called the military aid for Taiwan a "serious violation of the one-China principle" that would "send the wrong signal to the pro-independence separatist forces" in Taiwan.
"We urge the US to take practical actions to fulfil its commitment not to support Taiwan independence by not arming Taiwan in any way," she said.
Taiwan's incoming President William Lai said the aid package would "strengthen deterrence against authoritarianism".
Taiwan is a self-governing island and considers itself distinct from China, but Beijing views it as a breakaway province and hopes to bring it back under its own control.
TikTok ban
The national security package also includes a provision that could lead to a nationwide ban on TikTok.
The popular social media app's China-based parent company has nine months to sell its stake and find a US-approved buyer or see TikTok shut down across the US.
The statute gives the US president the option of extending the deadline by an additional 90 days, which means the latest the ban could take effect is nearly a year from now.
The TikTok provision drew bipartisan support, with lawmakers arguing that the Chinese government could invoke security laws to compel ByteDance to hand over data about the app's estimated 170 million US users.
TikTok has repeatedly said it has not provided, and would not provide, its foreign user data to the Chinese government.
What happened to the border funding?
On Saturday, the House of Representatives held a separate vote on a border-security bill that included conservative priorities, but it did not garner the two-thirds majority necessary to overcome a procedural hurdle.
In the Senate, several Republicans, including Ted Cruz of Texas and Marco Rubio of Florida, voted against the Ukraine aid package because it did not include increased funding for US border security.
Mr Cruz called it one of the toughest votes of his congressional career, but that the US needed to address the immigration issue first.
"I can't continue to allocate funds to secure Ukraine's border before we secure our own," Mr Cruz said.
In February, a group of Democratic and Republican senators proposed a foreign aid package that included significant immigration policy reforms and additional funding.
That effort collapsed, however, after former President Donald Trump and his congressional allies said the changes were not enough.
Comment: Meanwhile the looting continues in earnest in the UK, too: