The decision, first reported by NBC, is sure to enrage Turkey, a North Atlantic Treaty Organisation ally that views the YPG as a threat and has rebuked the United States for partnering with the group in its fight against extremists in Syria.
Trump is scheduled to meet his Turkish counterpart, President Recep Erdogan, at the White House next week.
Turkey views the Kurdish People's Protection Units, or YPG, as a threat and has criticized the United States for partnering with them in Syria.
But Ankara says the YPG is a terror outfit and the Syrian branch of the Kurdistan Workers' Party (PKK), who have waged an insurgency since 1984 inside Turkey that has left tens of thousands dead. The SDF is expected to spearhead the coming assault on the Islamic State capital of Raqqa. A full list wasn't immediately available, but officials had indicated in recent days that 120mm mortars, machines guns, ammunition and light armored vehicles were possibilities.
Neither the Trump administration nor the Barack Obama administration before it had made any secret of its intention to give the Syrian Kurds a primary role in isolating Raqqa leading up to the planned offensive.
It is a move that has always been under consideration at the Pentagon but has been delayed due to strong opposition from American NATO ally Turkey.
Dana W. White, the Pentagon's chief spokeswoman, said in a written statement that President Donald Trump authorized the arms Monday.
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The SDF, with enabling support from the U.S. and coalition forces, are the only force on the ground that can successfully seize Raqqa in the near future, she asserted.
White acknowledged Turkey's concerns, but said "the U.S.is committed to preventing additional security risks and protecting our North Atlantic Treaty Organisation ally".
On Tuesday, a United States official told Reuters the White House has approved supplying arms to Kurdish YPG fighters.
The United States on Tuesday announced it would supply weapons and military equipment to Kurdish fighters battling ISIL in Syria, despite intense opposition from North Atlantic Treaty Organisation ally Turkey. Last month in Washington, Turkish Foreign Minister Mevlet Cavusoglu told CBS News that USA support for that group crosses a red line.
Noting that the United States continues to prioritise its support for Arab elements of the SDF, White said Raqqa and all the liberated territory should return to the governance of local Syrian Arabs. The strikes were part of an ongoing counterterrorism operation targeting members of the YPG.
"Turkey has never and will never hit its allies anywhere, and that includes the U.S.in Syria", he said in a tweet posted shortly after Wednesday's radio interview.
The decision to arm the Kurds was announced just hours after Pentagon chief Jim Mattis met with a Turkish official in Denmark at an anti-IS coalition summit.