Ishak Mostefaoui, a former University of Westminster student, went to Syria in 2014, losing his British citizenship.
He either died while trying to escape or in serious disorder in the prison in Hassakeh, which houses Islamic State members, the BBC reported.
Mostefaoui, 27, was captured last year and held in the north-east Syrian prison, held by US-backed Syrian Democratic Forces.
He was the first British person to die in the prison, according to the BBC. Around 10 British men and 30 women are being held by the force.
Mostefaoui was among nine University of Westminster students to join the terrorist group. His father Abderrahmane said he was radicalised while at the university.
He was said to be a popular young man who loved football before telling his family in 2014 that he was going to Amsterdam for a few days.
After a month of silence before he called from Syria to tell them where he was. His father collapsed after hearing the news.
Mostefaoui's British citizenship was revoked in 2018. In 2019 his wife and child were killed and he was badly injured when his house was bombed.
The Foreign Office has told warned people against going to Syria since 2011 and has refused calls to allow prisoners to return to the UK.
A Government spokesperson said: "Those who chose to leave the UK and fight for, or support, Daesh [Islamic State] potentially pose a very serious national security risk.”
Around 900 people are thought to have left the UK to join Islamic State and other violent Islamist groups in Syria. Of those, 20 per cent have died, 40 per cent have come back to the UK and 40 per cent are still in the Middle East.