Ryan Lock is said to have died during an offensive by anti-IS forces in a bid to retake the northern city of Raqqa, considered to be the terrorist group’s capital.
The 20-year-old from Chichester, West Sussex, had joined Kurdish militia after telling his family he was going on holiday to Turkey in August.
Lock’s father, Jon, told the Guardian that his son was a “very caring and loving boy who would do anything to help anyone” and “had a heart of gold”.
The YPG said he had “crossed continents for the destiny of our people and humanity”.
Images posted on Facebook in October and November appear to show Lock holding an AK-47 and wearing military gear.
Mark Campbell, who was with a group of Kurdish activists who visited Lock’s family, told the BBC their main concern was that Lock’s remains are returned to the UK.
“We hope the UK Government will also use all their diplomatic powers to give practical assistance to the family to help bring Ryan’s remains home for burial,” he said.
A Foreign Office spokeswoman said: “The UK has advised for some time against all travel to Syria.
“As all UK consular services there are suspended, it is extremely difficult to confirm the status and whereabouts of British nationals in Syria.
“Anyone who does travel to these areas, for whatever reason, is putting themselves in considerable danger.”