The 11 tourists - from Germany, Italy and Romania - and eight Egyptians had been kept in Chad, not far from the border with Sudan. They are currently being taken to Cairo, the capital of Egypt.
"All the tourists and their Egyptian guides are in good physical and mental shape, and are on their way to Cairo," the agency quoted an official Egyptian source as saying.
A military source said they were being brought to Cairo in a military aircraft.
It was also reported that the Sudanese army had earlier killed six militants with links to the group that abducted the tourists and their guides, including a warlord the Sudanese say had ties to the rebel Sudan Liberation Movement.
The Egyptian Tourism Ministry earlier said that the kidnappers were "ordinary criminals" and not part of any terrorist organization.
Egyptian television quoted a high-ranking source as saying that no ransom had been paid for the release of the hostages.
The kidnappers had demanded 6 million euros ($8.8 million).
