Notter was seized along with two others on January 15 as they left a prison on the island of Jolo in southern Philippines.
While Vagni remains in captivity, Mary Jean Lacaba, a Filipina, was freed by the captors on April 2.
Notter will be flown to the city of Zamboanga later during the day where he will be reunited with colleagues from the International Committee of the Red Cross (ICRC).
Lieutenant-Colonel Edgar Arevalo, a military spokesperson, said Notter was found by troops in the interior of the remote island of Jolo.
Jesus Verzosa, the local police chief, said Notter was left behind when a police team chased a group of rebels who had tried to break the cordon around a guerrilla camp.
"The military pressure contributed to the recovery of the Swiss hostage," Arevalo said.
Local radio said Notter, wearing a green sweatshirt, black pants and boots appeared tired and haggard. He had lost some weight and was offered a glass of milk before doctors checked his blood pressure.
Notter was found walking near the main Indanan town early on Saturday, Richard Gordon, head of the Philippine National Red Cross said.
There had been reports of intense clashes around Indanan late on Friday, a day after the military said it was prepared to rescue the hostages.
The Abu Sayyaf group had threatened to behead one of the hostages unless Philippine government forces pulled back from around their positions on Jolo.
Fighters from the group have kidnapped a number of foreigners over the past decade, many of whom, according to the Philippine military, were released after the payment of large ransoms.
The fighters also killed an American hostage, Guillermo Sobero, in 2001. The following year a second American, Christian missionary Martin Burnham, was killed in a military attack that led to the rescue of his wife.
Abu Sayyaf is on the US government's list of foreign terrorist organisations, and small number of American forces have been rotating on Jolo island since 2003 to provide intelligence information to their Filipino counterparts.