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Kantner's body was retrieved Saturday in the southern province of Sulu, officials said.
"We will coordinate with the appropriate offices for the disposition of the remains of the victim," Western Mindanao Command Maj. Gen. Carlito G. Galvez Jr. said.
It was the second time Kanter had been abducted. He was held along with his partner, Sabine Merz, by Somali pirates for nearly two months in 2008.
Kanter was beheaded by Abu Sayyaf after a deadline to pay his ransom passed. The group had demanded 30 million Philippine pesos ($600,000) by February 26.
"The Federal Chancellor condemns the abominable act, which once again shows how unscrupulous and inhumane these terrorists are. We all must stand together and fight against them," said Steffen Seibert, spokesman for German Chancellor Angela Merkel.
Philippines President Rodrigo Duterte apologized to Germany for his troops' failure to prevent the killing.
"I am very sorry that the hostage, a national of your country, has been beheaded," Duterte said Tuesday. "There's a massive operation going on. We really tried our best. We have failed. That has to be admitted."
Philippine Presidential Peace Adviser Jesus Dureza said the government strongly condemned "the barbaric beheading of yet another kidnap victim."
"Up to the last moment, many sectors, including the Armed Forces of the Philippines, exhausted all efforts to save his life," he said in a text message to CNN. "We all tried our best. But to no avail."
Abu Sayyaf announced last November that they had kidnapped Kantner and his partner in the waters off Malaysia's Sabah state, according to Philippine officials.
Merz was shot and killed by the militants soon afterward.
In September, Abu Sayyaf freed a Norwegian man it had held captive for almost a year, according to CNN Philippines.
War against Abu Sayyaf
The beheading emerges as the Philippine government wages a war against Abu Sayyaf, based in the restive Muslim-majority province of Mindanao in the country's far south.
Abu Sayyaf is a violent extremist group of some 200 to 400 members that is largely fragmented.
The Philippines is a predominantly Catholic country, but the south has historically had a large Muslim population. Abu Sayyaf's stated aim is to establish an independent Islamic state on the southern island of Mindanao.
The group first became active in the early 1990s and was responsible for bombings across the southern Philippines and in the Malaysian state of Sabah.
The seas around the Philippines are the most pirated in the world, according to data producer IHS Markit.
CNN's Andreena Narayan, Buena Bernal and Justin Heifetz contributed to this report.