President Obama opted to hand control of the weapons program to CIA in a classified order issued by the White House on Thursday, the Journal reports.
Pentagon press secretary George Little declined to comment on the arms program on Friday, deferring all comment to the White House.
CIA officials famously coordinated and ran the program to arm the Afghan mujaheddin in the 1980s.
Agency operatives delivered an assortment of small arms and Stinger surface-to-air missiles to Afghan warlords, who were battling to push out the Soviet army from the country.
The White House initiated the CIA-led Syrian weapons program a day after U.S. intelligence officials concluded the Assad regime had used chemical weapons against opposition forces.
Assad's use of those weapons crossed a "red line" with the Obama administration, prompting the president to approve the arms supplies to Syria's rebels.
"We will be consulting with Congress on these matters in the coming weeks," Deputy National Security Adviser Ben Rhodes said Thursday.
"Put simply, the Assad regime should know that its actions have led us to increase the scope and scale of assistance that we provide to the opposition."
Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) said on Thursday that Obama needed to do more than just supply weapons to the rebels in Syria.
“Every bone in my body knows that simply supplying weapons will not change the equation,” McCain said on the Senate floor. “The president better understand that just supplying weapons will not change the balance.”
But Rep. Mike Rogers (R-Mich.), the chairman of the House Intelligence Committee, said he was pleased with the declaration.
"These efforts have the potential of turning the tide once and for all against the Assad regime to deliver a peace negotiation," he said.