David Mitchell, his wife Caroline, and their 14-year-old son, Ben, were last night travelling to the capital Sanaa and were expected to spend the evening in a hotel before meeting the British ambassador.
The Mitchells were kidnapped on 17 April by five members of the Bani Dhabyan tribe and held near the town of Knoum, 100 miles from the capital.
Mr Mitchell, 48, an English teacher with the British Council, was driving his wife and son to the airport in Aden to put them on a flight home after they had visited him during the Easter holidays.
Sheik Mohammed al-Ruwaishan, who negotiated the family's release, promised their abductors that they would not be prosecuted and that their demands would be looked into by the government, the official said.
The tribesmen had demanded an undisclosed ransom as well as the construction of more roads in their area. They also asked the government to return a four-wheel drive vehicle that was seized from them in March.
They agreed to release the Mitchells after troops, armed with automatic weapons, who were sent to Knoum to put pressure on them, were dispersed.
The family had been receiving food, medicine and clothing through tribal mediators.
Mr Mitchell has worked in Yemen for two years but the rest of the family returned to Sidley, east Sussex, last year. A Foreign Office spokesman said: "We are aware of reports that the Mitchells have been released and we are trying our best to check them out."
Pat Reigh, a church elder and friend of Mrs Mitchell, who is a deacon at Sidley Baptist Church, said the family's friends were awaiting confirmation of the reports.
"It will be thrilling if it's true, it really will," he said.
"Over the last two weeks the church has been meeting twice a day to pray for the family, so they have been very much in our thoughts." Large swaths of Yemen are virtually lawless and ruled by armed tribesmen who kidnap foreigners to demand money or press for concessions from the government.
Eleven foreigners have been taken hostage so far this year; all were released unharmed.Reuse content