Luke Symons, 30, from Cardiff, Wales, was taken to Oman's capital Muscat and will be reunited with relatives in the UK in the next few days, his family said.
The others released were seven Indian citizens, a Filipino, an Indonesian, Ethiopian and one person from Myanmar, said Oman's foreign ministry.
"The whole family is ecstatic," said Mr Symons's grandfather, Robert Cummings. "Luke has gone through hell. But as soon as he comes home and he is settled we are going to have the biggest party in Cardiff."
Mr Symons was arrested at a checkpoint in Taez, a city in the country’s south-west, in 2017 and accused of spying for the UK on the basis of the British passport that he was carrying at the time, his family believes.
He was beaten, repeatedly questioned and held in prison despite never being charged with a crime.
Mr Symons, a Muslim, travelled to Yemen in 2012 to increase his knowledge of Islam. He married a local woman and has a young son. The couple tried to leave after the war started but Mr Symons was unable to secure documents for his wife to leave before he was arrested.
He and his family have always denied the accusations against him and say that he has been used as a bargaining chip by the Houthi rebels for financial reasons.
A senior Houthi official ordered his release in December 2018, saying that there was no evidence against him, but the order was never carried out.
His family said that he was released from the prison in Sanaa on Sunday and taken to the airport where he was reunited with his wife and child.
They are undergoing health checks in Muscat, said Mr Cummings. He said it was not clear what deal had been struck with the Houthi regime to secure his release.
Oman said the 12 foreigners along with Mr Symons' wife and child, 5, were taken by an Oman Royal Air Force plane to Muscat, in preparation for their return to their countries.
"They have just landed, they are in a hotel and everything is secure," Mr Cummings told The National. "He is with his wife and child and he should be home within the next 72 hours."
The British government thanked Oman and Saudi Arabia for helping to secure his release.
UK Foreign Secretary Liz Truss said: “I am pleased that Luke Symons, who was unlawfully detained, without charge or trial since 2017 in Yemen, has been released.”
“Luke was 25 when he was unlawfully detained by the Houthis. His son was only a few months old at the time.
“He was allegedly mistreated, in solitary confinement, and refused visits by his family.
“We thank our Omani and Saudi partners for their support in securing his release. I pay tribute to our excellent staff for their hard work in returning Luke home.”
The case of Mr Symons has been repeatedly raised by his MP, Kevin Brennan, who welcomed the news of his release.
"This is terrific news — after 5 years finally my constituent Luke Symons has been released from captivity," he said in a Tweet.
The supporters of Mr Symons had hoped that he would be freed during a prisoner swap in 2020 but the Houthis reneged on the deal, according to UK officials.
Mr Abdulsalam had assured a British minister at a meeting in Muscat that Mr Symons would be released during an exchange of hundreds of prisoners in October 2020. But the Briton was not included in the group handed over.
Sunday's releases came after the warring sides in Yemen's seven-year conflict agreed to a nationwide truce for the first time in years, under a UN-brokered deal.