Sheik Awadh Bin al-Wazir, a member of parliament and a key negotiator, said the kidnappers had agreed to free the hostages before Saturday morning under the deal.
"We have agreed to the kidnappers' demands after personally consulting with the president and government officials," al-Wazir told The Associated Press.
TheJuergen Chrobog, his wife and three children on Wednesday, seeking the release of five jailed fellow tribesman.
Chrobog, 65, served as deputy foreign minister in Gerhard Schroeder's government, which left office in November. He had been German ambassador to Washington.
Al-Wazir said the negotiations had taken place on a mountaintop in the Rafadh district of Shabwa province, where the abduction occurred.
He said the government agreed to the deal to "speed the hostage release and to keep this issue as a one that is between Yemenis, as well as out of our sense of humanitarian and moral responsibility."
German Foreign Minister Frank-Walter Steinmeier spoke Friday with his Yemeni counterpart and called for a negotiated solution, Foreign Ministry spokesman Martin Jaeger said. "The (German) government is calling for a violence-free solution in this case, and the Yemeni side has assured us of this."
The kidnappers had demanded the government release five members of their al-Abdullah bin Dahha tribe who were detained and standing trial for allegedly killing two members of a rival tribe in October.
The Chrobog family's tour operator, Mohammed Abdulkarim Abu Taleb, told a German television channel on Thursday that the whole group was in good condition. Taleb said he had contacted the hostages through the mobile phone of their tour guide who was seized with the family.
Tribesmen frequently kidnap tourists in an attempt to force concessions from the government in Yemen, a poor, mountainous nation on the southern tip of the Arabian peninsula where state control in outlying areas is shaky.
Hostages are usually released unharmed in Yemen, but several were killed in 2000 when security forces carried out a botched raid to free them.