A video posted by the extremist Abu Sayyaf group, which was monitored by SITE, showed German hostage Jurgen Kantner being killed by a knife-wielding man.
The video appeared to confirm preliminary reports received by Philippine government officials that the mercenary group had slain Kantner.
The Abu Sayyaf, blamed for the worst terror attacks in Philippine history, had previously demanded a ransom of 30 million pesos (USD 600,000) by Sunday to spare the 70-year-old.
Government envoy Jesus Dureza, who was negotiating for Kantner's life, told AFP he had heard of the video, adding that it confirmed earlier reports that Kantner had been killed.
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Kanter was abducted from his yacht, the Rockall, in waters off the southern Philippines last year.
The vessel was found drifting on November 7, with the body of Kantner's female companion, Sabine Merz bearing a gunshot wound inside.
The couple had previously been kidnapped and held for 52 days in Somalia in 2008 before they were freed, reportedly after a huge ransom was paid, press reports said.
The Abu Sayyaf, whose leaders have pledged allegiance to the Islamic State movement in the Middle East, have been kidnapping foreigners and Christians for decades, holding them for ransom in the jungles of the strife-torn southern Philippines.
The group, formed from seed money provided by a relative of Al-Qaeda mastermind Osama bin Laden, also carried out the bombing of a ferry in Manila Bay in 2014 that claimed 116 lives in the country's deadliest terror attack.