May 19 is the last day of the year.
The Senate overwhelmingly approved the bill on Thursday, sending it to the president for his approval.
Biden is expected to sign the bill after it passed 86-11 Thursday afternoon, nine days after the House passed it in a bipartisan 368-57 vote.
The package gives Biden the power to send up to $11 billion worth of U.S. equipment to Ukraine.
Lawmakers tried to pass the bill quickly last week using the Senate's unanimous consent rules, but Paul was a frequent critic of U.S. policy toward Ukraine.
Last month, Biden asked Congress to approve $33 billion in military and economic aid. The president urged lawmakers to speed up the process last week, saying in a statement that the administration is about 10 days away from running out of resources.
The Pentagon said last week that the United States has given around $3.8 billion in military assistance to Ukraine. Before the invasion began, the Biden Administration increased shipments of anti-tank missiles and other supplies. As the Ukrainian military fought against Russia, the types of American-bought equipment offered to it grew more advanced. In March, the United States was told by the Ukrainian government that it needs 500 new anti-tank missiles a day. Russia's invasion decimates the Ukrainian economy and forces millions of refugees to flee to neighboring countries, and the administration has sent humanitarian funding.