But there are still believed to be up to 100 under-age fighters in the ranks of the YPG (People's Protection Units) and its women's arm, the YPJ (Women's Protection Unit).
Those children are cut off in a part of northern Syria where the Kurds are trying to stem an assault by jihadists from the Islamic State (which was formerly known as the Islamic State of Iraq and Levant), which already controls swathes of Syria and Iraq.
Decrey Warner said that YPG and YPJ signed a formal pledge on Saturday, along with the self-declared government of Syrian Kurdistan, not to accept under-age recruits in the future.
"We undertake to no longer use any under-18 children in hostilities, including for combat, spying, guarding tasks or supplying combattants, and we won't admit any under-18s as combatants in our ranks," Kurdish defence official Abdulkerim Sarukhan said in a Geneva Call statement.
The Kurds have controlled three pockets of northwestern, northern and northeastern Syria since government troops pulled out in 2012, a year after the country tumbled into civil war.
They have focused on keeping order and holding off outside attacks.
Their forces' combined strength is estimated at up to 30,000, protecting territories with 2.5 million residents and 500,000 people who have fled other parts of Syria.
"We've been negotiating for months over the presence of children in their ranks," Decrey Warner told reporters.
- 'Two or three' more could sign -
She and other Geneva Call representatives travelled from Iraqi Kurdistan to sign the accord, and staff members remain there to monitor its implementation.
Turkey's PKK Kurdish rebels made a similar pledge last October, and Geneva Call has also inked deals with Kurdish groups in Iran.
It previously has brokered non-recruitment deals with rebels in countries including India, Myanmar and Sudan.
Geneva Call's programme director, Mehmet Balci, said it had put out feelers to a range of rebel groups in Syria from 2012 onwards, including the mainstream Free Syrian Army.
Balci said that "two or three" groups had expressed an interest in signing a pledge, but did not identify them for reasons of confidentiality.
"We're assessing their capacity for implementation," he explained, adding that a proper chain of command was a key issue.
The number of child soldiers in Syria is unknown, but the Violations Documentation Centre, a organisation close to the opposition-in-exile, reported that 194 "non-civilian" children have been killed since September 2011.
In a report last month, Human Rights Watch accused rebels of fielding children as young as 15 in their fight to oust President Bashar al-Assad.
The New York-based watchdog said teenagers were often recruited via free schooling programmes, notably by radical Islamists.
Others joined up to follow friends or family, or enlisted after Assad's crackdown on peaceful protests calling for political change that sparked the conflict in March 2011.