Anna Campbell was killed last week in the Afrin enclave, said Nisrin Abdallah, a spokeswoman for the Kurdish Women's Protection Units (YPJ).
"She died on March 15, 2018 in Turkish shelling" on front lines around Afrin city, Abdallah told AFP, adding that Campbell was 27 at the time of her death.
She is thought to be the first British woman killed fighting alongside the Kurdish militia in Syria.
"We learned of her death yesterday and communicated with her parents," Abdallah said, confirming that Campbell was from Lewes in East Sussex.
Ankara and allied Syrian rebels began their assault on the Afrin region on January 20, seizing most of the canton before capturing its urban centre on Sunday.
Anna Campbell (right), a British woman who died fighting with the Kurdish armed unit in Syria. Source: Press Association
They swept into the city after the fighters from the YPJ and its male counterpart, the People's Protection Units (YPG), appeared to withdraw.
Abdallah said Campbell joined the YPJ in May 2017.
"After the attack on Afrin, she insisted on being sent there," Abdallah said.
"We discussed with her a lot, but she gave us an ultimatum: either I quit the revolution or I go to Afrin," she added.
Hundreds of foreign fighters have joined the YPG and YPJ in Syria, with many saying they wanted to back a "revolution" for participatory democracy and women's rights.
Most have fought alongside the Kurdish militia in its battle against the Islamic State jihadist group.
'Shocking' Turkish attacks
Later on Monday, the YPJ published footage of Campbell, apparently filmed after she had completed a training course with militia but before she was deployed to Afrin.
In it, the woman appears in military fatigues with a red handkerchief wrapped around her hair, which she seemed to have dyed black.
"I joined because I wanted to support the revolution," Campbell tells the camera, saying she had previously fought IS in Syria's eastern Deir Ezzor province.
"Now I'm very happy and proud to be able to go to Afrin and be able to do this. The attacks of the Turkish state against the revolution, against the Kurdish people, and the people of Kurdistan are very shocking and heavy," she says.
Her father, Dirk Campbell, told the BBC that Anna had dyed her hair black to blend in.
People attend a vigil honouring Anna Campbell in her home town of Lewes, East Sussex. Source: Press Association
"With fair hair and blue eyes they knew she would stand out, but she dyed her hair black and persuaded them to let her go," he said.
When he heard his daughter was in an area being bombed by Turkey, Dirk emailed his MP Maria Caulfield, asking her to put pressure on Ankara to halt shelling.
Several Britons have died in fighting alongside the Kurdish forces, including British fighter Jac Holmes, from Bournemouth in southern England.
He was killed in IS's de facto capital Raqa in October, just days after Kurdish-led forces ousted the jihadists from the city.
At least two other foreign fighters have been killed in the Afrin assault, according to the YPG.
French national Olivier Francois Jean Le Clainche, 41, and Spanish national Samuel Prada Leon, 25, were killed fighting in the Afrin enclave in February.
