Hassan Muhammad al-Dhaman said on Tuesday he had released the couple after receiving a promise from Yemeni officials to look into the case of his imprisoned brother.
"We have released them. They are on their way back," he said. Yemeni security officials confirmed the Swiss were free.
Al-Dhaman and fellow tribesmen kidnapped the two tourists to press for the release of al-Dhaman's teenage brother, arrested on charges of stealing a car, government and tribal sources said.
On Monday, a Swiss Foreign Ministry statement said its two nationals had been freed and were safe and well after efforts by the Swiss officials in Yemen and Saudi Arabia and by the Yemeni authorities to release them.
In a second statement on Tuesday, the Swiss ministry said the release had in fact been completed on Tuesday morning.
An official said Monday's announcement had been premature.
The Swiss government did not pay any ransom, a spokesman said.
"Switzerland does not let itself be blackmailed and does not pay ransom"
"Switzerland does not let itself be blackmailed and does not pay ransom," he said. "We don't know what was agreed to by the Yemeni authorities."
While warning tourists of travel risks in Yemen, the spokesman said it was possible that the newly freed couple would continue their journey.
"I'm not a spokesman for the couple but it could be that after a brief recovery they could continue with tourism," he said.
The Yemeni official said they were taken in the mountainous Maarib province, east of the capital Sanaa.
Tourists have often been seized by armed tribal groups in Yemen, a poor country at the tip of the Arabian Peninsula where central government control is weak in many areas. Most have been released unharmed after negotiations.