He was said to be Mehdi Hassan, 19, from Portsmouth, Hampshire, who travelled to the country with four other men in October last year.
A photo of his body emerged on Twitter on Friday and his family confirmed earlier to their local mosque they had received news of his death, the BBC reported.
A Foreign Office spokesman said: “We are aware of reports of the death of a British national in Syria.
“The UK has advised for some time against all travel to Syria, where all UK consular services are suspended. As we do not have any representation in Syria, it is extremely difficult to get any confirmation of deaths or injuries, and our options for supporting British nationals there are extremely limited.”
It emerged on Tuesday that a third Portsmouth man, Manunur Roshid, had been killed.
The 24-year-old was understood to have joined up with fighters from the Islamic State (IS). Two of his companions, Ifthekar Jaman, 23, and Muhammad Humidur Rahman, 25, had already died.
Speaking about the latest death, Abdul Jalil, chairman of the Portsmouth Jami Mosque, told the BBC: “It has been confirmed with the family that he has died. Right now they are very upset.
“I am saddened and again shocked for the community about this news.”
Hassan, who went by the name of Abu Dujana in Syria, attended a private Catholic school in Hampshire.
As a teenager he was a keen reader of Roald Dahl and Harry Potter and had intended to study international politics at Surrey University.
But instead of starting university in September last year, he travelled to Syria to fight with four other young men from the Portsmouth area – to the horror of his shocked parents.
Last night his family issued a statement in which they said Hassan had a “good heart” and was trying to “help Syrians”.
The family also suggested that the teenager had considered returning home from Syria but was worried by the threat of prosecution on terror charges.
The statement read: “Mehdi was a loving boy with a good heart wishing to help Syrians. In recent months he had expressed the intention to return home but was worried about the repercussions. This is a tragedy and a lesson. We request that the family be left to grieve.”