The move is seen as controversial, given Russia's opposition to the rebels and Moscow's strong support for the regime of Syrian President Bashar al-Assad.
"It's a strategic mistake.... (support for the rebels) was a pressure point on Assad and a pressure point on the Iranians... and the Russians," according to Bob Baer, CNN Intelligence and security analyst and former CIA operative.
"It looks like, to me, that he just gave that as a gift to Vladimir Putin for no quid pro quo and that's not the way diplomacy works. We should've used this, we should've demanded, for example, safe zones so the Sunnis wouldn't get hit from the air... so this is just inexplicable, why he would do this.
"He's lost his pressure point... it's crazy, frankly, I've never seen anything like it."
Former US President Barack Obama signed the covert directive in 2012, US officials told CNN at the time
The then-administration said it would step up its assistance to the opposition in the wake of a 2012 failure by the UN Security Council to agree on tougher sanctions against Syrian President Bashar al-Assad's regime. Russia and China vetoed those measures.
CIA-funded weaponry started flowing to Syrian rebel groups
the following year.
The Obama administration had resisted arming the rebels, citing concerns about the infiltration of extremists groups who could possibly use those weapons against other targets, CNN reported at the time
Questions over Putin-Trump talks
The Post reports that the decision to remove the CIA's support for the rebels came nearly a month ago, ahead of Trump's bilateral meeting with Russia President Vladimir Putin
on the sidelines of the G20 talks in Hamburg in early July.
However, such a move is likely to come under scrutiny, given how closely it aligns with Russia's support of Assad's regime.
The timing of the step, given multiple US government investigations into the Trump campaign's links to the Kremlin, will also raise eyebrows.
"The context of this is, at the meeting in Hamburg, Trump let Putin go on the hacking," Baer said. "He's not addressed the hacking and rather than taking some sort of retaliation against Putin for the hacking, he gave him a gift. The optics of this couldn't be worse."
Following the Hamburg meeting between Trump and Putin, a limited ceasefire in the southwest of Syria
was implemented, but US officials who spoke to the Post said that the discontinuation of the CIA program was not a condition of that development.
It was recently confirmed by the White House that the two leaders also had a second, previously undisclosed side conversation
at a social dinner for G20 leaders.
At a White House briefing, Assistant Press Secretary Sarah Huckabee Sanders was asked if Trump was ending the CIA program. She said she couldn't comment "at this time." Sanders also said it did not come up at the dinner with Putin at the G20, as far as she was "aware of."
It's unclear what assurances, if any, Trump could have offered Putin in private. The pair spoke through the Kremlin's official translator.
Kremlin: No comment
The Kremlin also declined to comment Thursday on the report that Trump had ended the CIA program in Syria.
Asked about it during a regular call with reporters, Kremlin spokesman Dmitry Peskov said: "I won't comment this on behalf of Kremlin. No comment on that."
Asked if the issue of US support for Syrian rebels had come up during the G20 meeting between Trump and Putin, Peskov said "no."
Trump has spoken about ditching the Obama-era program in the past. In November he spoke to the Wall Street Journal
about the arming of rebels, saying that he didn't think it was productive to be fighting Syria which is fighting ISIS.
"I've had an opposite view of many people regarding Syria," he said in the interview. "My attitude was you're fighting Syria, Syria is fighting ISIS, and you have to get rid of ISIS. Russia is now totally aligned with Syria, and now you have Iran, which is becoming powerful, because of us, is aligned with Syria.
"Now we're backing rebels against Syria, and we have no idea who these people are."
The reported decision, while a big change in policy, could be seen as an acceptance that the Obama-era CIA program -- despite costing hundreds of millions of dollars -- has largely failed.
After Russia became directly involved in the Syrian civil war in support of Assad in September 2015, with planes, troops and cruise missiles, its efforts dwarfed those of the United States.
Since then those rebel forces have lost ground steadily, including losing control of parts of the city of Aleppo late last year, and have now been pushed into a corner by Syrian government forces.
Trump administration U-turn
In April, following Assad's chemical attack
on his citizens -- an attack for which he continues to deny responsibility, putting the blame instead on rebel groups -- US ambassador to the UN Nikki Haley told CNN
that removing Assad from power was a priority, cementing an extraordinary U-turn in the Trump administration's stance on the embattled leader.
Trump, before his election, described fighting ISIS and seeking Assad's removal at the same time as "idiocy.
According to the Post, the decision to stop CIA funding for the program does not impact the Pentagon-led effort to work with US-backed Syrian rebels in the fight against ISIS.
US-backed Syrian Democratic Forces are currently fighting their way into Raqqa, the self-proclaimed ISIS capital in northern Syria.