Anna Campbell was volunteering with the Kurdish Women’s Protection Units (YPJ) – the all-female brigade of the Kurdish People’s Protection Units (YPG) – in the besieged city of Afrin when she died on Thursday.
It is feared she was killed by a Turkish airstrike.
The 26-year-old from Lewes in East Sussex is the first British woman to have been killed in Syria fighting with the Kurds.
Seven other Britons have died in the country fighting alongside Kurdish groups.
Her father, Dirk Campbell, said he had tried to stop her travelling to Syria.
He last heard from her two months ago when she told him she would not be doing any fighting – but Mr Campbell said he had suspected she was.
He described her as “very positive, optimistic and happy” and a person who “knew she was doing something meaningful”.
“She was trying to make a better world and knew she was risking her life,” he said.
Mark Campbell, co-chairman of the Kurdistan solidarity campaign, described Ms Campbell, who is no relation to him, as an “inspiration” and a “hero”.
“Anna is a woman who seemed to have more humanity in her little finger than the whole of the international community,” he said.
“I did not know her but I met with her father this morning. I have the utmost respect and condolences for her family.”
Dozens of children have been killed and tens of thousands of people have been displaced from Afrin, according to the UN, as the conflict in Syria enters its eighth year.
The EU’s foreign policy chief criticised Turkey’s military offensive in northern Syria on Monday.
Federica Mogherini said international efforts in the war-savaged country are supposed to be aimed at “de-escalating the military activities and not escalating them”.
The Syrian government says the Turkish invasion has nothing to do with protecting its borders and is instead simply a “land grab”.
Turkey denies it is targeting civilians, or is engaged in expansionism.
It says its campaign – codenamed Operation Olive Branch, which saw it launch incursions into northern Syria – is about protecting its territory from Kurdish terrorists.
Turkey regards the YPG as a terror group and an offshoot of the separatist PKK which it has been battling for decades inside its own borders.