James Le Mesurier's body was found near his home in the Beyoglu district by worshippers on their way to a mosque, the state-run Anadolu news agency reported.
The Istanbul governor's office said "comprehensive administrative and judicial investigations" had been initiated into Le Mesurier's death.
Anadolu said police established that no one had entered or left his home, and they believe he may have fallen to his death.
The White Helmets confirmed his death on its Facebook page.
"The family of the Syrian Civil Defense extends its deepest condolences to his family, and we express our deepest sorrow and solidarity with his family," the group said.
In New York, Karen Pierce, Britain's ambassador to the U.N., paid tribute to Le Mesurier, calling him a "true hero" and a "real humanitarian."
"He really deserves our respect," she said, adding that the White Helmets have "saved countless of people from the ravages of (Syrian President Bashar) Assad's forces and paramilitaries."
"The world, and Syria in particular, is poorer for his loss," she said.
The Syrian government and its allies, including Russia, have been critical of the White Helmets volunteers, accusing them of being agents of foreign powers, terrorists working in rebel-controlled areas and of staging chemical attacks.
The group, which has had more than 3,000 volunteers in opposition-held areas, says it has saved thousands of lives since 2013 and documented Syrian government attacks on civilians and other infrastructure.
Last week, Russian Foreign Ministry spokeswoman Maria Zakharova had accused Le Mesurier of being a former British agent who has "been spotted all around the world, including in the Balkans and the Middle East."
"Given the role of the West in undermining stability in these regions, it is not difficult to assume what the British intelligence officer did there," she said.
Pierce said Monday that such allegations were "categorically untrue." She said that Le Mesurier had been a soldier at one point but was no longer on active duty when he founded May Day Rescue and the White Helmets.
Turkey's private DHA news agency said authorities were investigating whether Le Mesurier had killed himself, and that he had been taking antidepressants. Anadolu also reported that Le Mesurier's wife told police her husband had been taking medicine to treat "extreme stress" and that they had moved to the neighborhood to be close to a health center.
Anadolu said his wife told police they had been up until 4 a.m., then took sleeping pills. She was woken by the doorbell less than two hours later and saw her husband's body from the open window of their third-floor apartment.
DHA said Le Mesurier's body was awaiting an autopsy.
Hulya Hemen, a local shopkeeper, described Le Mesurier as a polite person who would come to her shop to buy cigarettes.
"When he talked, for example, he could speak Turkish, Arabic, English. It was obvious he was cultured," she said.
Fraser reported from Ankara. Associated Press reporters Zeina Karam in Beirut, Jim Heintz in Moscow and Edith Lederer in New York contributed to this report.