Their abductors allegedly took them to neighbouring Sudan.
Amr El-Khaky, Al Jazeera's correspondent at the airport in Cairo, said: "The chopper taking is now taking the hostages to military hospital in Cairo to receive treatment, and officials about to speak about the operation that freed them and conditions in which they were held.
"We've seen officials from the Italian and German embassies, the Egyptian tourism minister, and military officials - one of whom co-ordinated the hostage rescue."
Hussein Tantawi, the Egyptian defence minister, said "half of the kidnappers were eliminated" in the raid, the official MENA news agency reported.
"Just before dawn two helicopters flew in special forces from the elite Lightning Brigade who freed the hostages," an Egyptian security official said.
"There was a gunfight during which half of the 35 kidnappers were killed and the rest escaped," he said.
"We cannot yet relate the dynamics [of the release] but we can deny with certainty the payment of any ransom," Frattini said on Italian television from Serbia.
"It was a most professional operation, and obviously we thank our German friends who worked with us, as well as Egypt and Sudan," he said.
"We should recognise that we obtained this result thanks to the professionalism and effectiveness of our secret services, our special forces," he said.
State-run Egyptian television said on Monday that the tourists had been rescued by Sudanese and Egyptian forces near the Sudanese-Chadian border.
Franco Frattini, the Italian foreign minister, suggested Italian and German special forces were involved in the rescue.
Frattini told the Sky TG24 news channel that Sudan and Egypt carried out "a highly professional operation'' with the "intervention of Italian intelligence and experts from the special forces'' from Germany and Italy.
The rescue came a day after Sudan said its forces had killed six of the kidnappers in a remote desert in southern Egypt.
The Italian foreign ministry has also confirmed the news of the release.
The kidnappers had reportedly demanded up to $15m in ransom for releasing the hostages.
Egypt's state television quoted an official as saying no ransom had been paid.