The Muslim community-led convoys became unwitting vehicles for the plan to fund terrorism, the Old Bailey heard.
One of the targeted aid missions included Alan Henning, the Eccles taxi driver later kidnapped and murdered by militants from so-called Islamic State.
Syed Hoque, 37, of Stoke-on-Trent, and Mashoud Miah, 27, of east London, were both convicted of funding terrorism.
Hoque was found guilty of two charges of funding terrorism and Miah was convicted on one count by majority following a trial.
A third defendant, Huddersfield charity worker Pervez Rafiq, 46, was cleared of involvement in their plans. Mohammed Hussain, 30, of east London, was also found not guilty.
This is the first court verdict showing that some aid convoys were abused.
Both Hoque and Miah were remanded in custody. The pair are due to be sentenced on 13 January.
The outcome of the case raises questions about whether charities organising humanitarian convoys, to transport aid and medical supplies to foreign conflict zones, have the means to identify potential abuse – and whether they are capable of stopping it.
The huge aid convoys dried up amid government pressure following Alan Henning’s kidnap in December 2013 and reports that British jihadists had used them as cover.
The Old Bailey heard that Hoque’s nephew, Mohammed Choudhury, had left for Syria in early 2013 and ultimately joined the al-Nusra Front, the largest jihadist organisation in the war zone after so-called Islamic State.
Using social media, he asked Hoque for cash to buy a specialist sniper rifle and the pair discussed in detail the type of weaponry he needed.
Hoque, a former probation officer, agreed to supply £3,000 with the help of co-defendant Mashoud Miah who, in 2012 and 2013, was moving in and out of the region.
In July, the men joined a massive British aid convoy and set off to hand the cash over to the fighter.
The humanitarian mission involved 100 vehicles including ambulances and large lorries packed with supplies. There was no suggestion in the trial that the convoy’s organisers knew of the pair’s plans.
After the cash was delivered, Choudhury maintained contact with Hoque, later telling him of his desire to kill disbelievers. The court heard that Hoque replied: “No mutilating, just beheading.”
Hoque admitted supplying the cash – but told the jury he wanted his nephew to be able to defend himself and did not believe he was breaking the law.
He supplied a further tranche of £1,500 which was taken into Syria in the December 2013 aid convoy which had included Mr Henning.
The taxi driver was kidnapped by IS militants after crossing into Syria with other aid workers.
There was no suggestion in court that any of the defendants were involved in the kidnapping.
When Mr Henning’s kidnap was publicly revealed the following September, the third defendant, Pervez Rafiq, made a high-profile appeal directly to IS for mercy.
Mr Rafiq, one of the co-ordinators of the convoys, had been on the same December 2013 aid mission as Mr Henning and prosecutors alleged he had a wish list of equipment to aid fighters.
But the jury cleared Mr Rafiq of that charge after hearing during the trial that he had spoken to MI5 which had been gathering intelligence on infiltration of convoys.
During the trial it emerged that Mr Rafiq had never met Hoque – although he had come across Miah at an aid headquarters in Turkey.
Described by his defence team as a “prolific fundraiser”, Mr Rafiq made six trips to Turkey delivering aid and raised £200,000 for the two key Syria convoy charities.
According to his account, which was unchallenged by the prosecution, MI5 approached him asking for help in return for £30,000.
The trial heard that Mr Rafiq was so scared by the approach that he recorded one conversation with a purported MI5 officer called “Ben”.
The officer told the defendant: “I think really your heart is in the right place but you are in circumstances that are generally above and beyond your own control.”
Mr Rafiq says he did not become a paid informant but assured the Security Service that if he came across wrongdoing he would tell the police.
When he was later arrested, he said in an interview that IS were “nutters”.
In February 2014, the Charities Commission issued an alert to all Syria aid organisations that they were at risk of being exploited and urged them to properly vet volunteers and the end use of their aid.
In a statement, the commission told the BBC that it is still investigating the governance of four Syria aid charities – including Children in Deen and Al-Fatiha Global, which were exploited by the men convicted in this trial.