Dean Carl Evans, 22, from Reading, died on 21 July during fighting in the city of Manbij, Kurdish reports suggest.
His father, John, posted a statement on social media confirming the death and added: "He was loved and will be missed by all his family and friends".
The Foreign Office is looking into reports of the death - the second involving a Briton fighting against IS.
In a second post, Mr Evans, who lives in Oxford, said: "I would like to say a massive big thank you to all my friends and family who sent their condolence for the loss of my son.
"He would have been very proud and would have regarded you all as his brothers and sisters, thank you again."
Mr Evans was one of many foreign volunteers who joined the People's Defence Units (YPG) - the Kurdish military force fighting in northern Syria.
Dean Carl Evans has become the second British man to die in the fight against IS with the Kurds in Syria.
The first UK casualty, Erik 'Kosta' Scurfield, died during fighting to take back the strategic Til Hamis town in the Hasakah province in north-eastern Syria.
Mr Evans died fighting for another strategic town, called Manbij, in north-western Syria.
Kurdish YPG units were among forces which started an attack on Manbij, which has become the new epicentre of the fight against the IS Group in Syria, in April this year.
Capturing Manbij from IS would cut the corridor between the town and the group's de-facto capital city, Raqqa, in central Syria.
A UK-based pro-Kurdish activist, Mark Campbell, told the BBC Mr Evans had travelled to Syria in 2015 and again in March this year.
He said his contacts near Manbij told him Mr Evans had been fighting on the frontline and sheltering behind a wall when he was fatally struck by a bullet.
In a statement, the YPG described Mr Evans as a "man with the noblest of intentions who planted a seed of love into the hearts of [his] friends and all the peoples of Rojava [Western Kurdistan]".
Jac Holmes, an IT worker who left the UK to join the fight against IS, posted a tribute to Mr Evans online.
He said the pair had met twice, and described Mr Evans as a "great man" who had "moulded himself" into a soldier during his time in the Middle East.
A number of well-wishers replied to John Evans' post on social media announcing his son's death.
One user said: "Feel for you soldier. Sorry to hear your sad news John. My thoughts go to you and your family. RIP young man."
Another added: "So so sorry to hear your sad news John. Keep strong and remember we're all here if you need someone to talk to."
A statement from the Foreign Office said: "As all UK consular services [in Syria] are suspended, it is extremely difficult to confirm the status and whereabouts of British nationals in Syria."
It said it had advised for some time against all travel to Syria.
"Anyone who does travel to these areas, for whatever reason, is putting themselves in considerable danger."
A British man has reportedly died fighting with Kurdish forces against so-called Islamic State in Syria.