The men are among 10 Muslims, eight of whom are British, who were found guilty last month of forming a terrorist group and planning sabotage activities in the Arab state.
"They were given their freedom today and they are expected to leave the country within the next few days," said David Pearce, the British consul-general in Aden, who collected them from prison yesterday morning.
Said al-Aqel, the chief prosecutor in Aden, confirmed the release and said the men were free to leave Yemen whenever they wanted. "We handed them their passports in the presence of the British consul- general and their lawyer," he said, adding that he thought they might leave on Friday.
Rashad Yaqoob, a defence lawyer from the human rights organisation, the Legal Studies Institute, said: "I am relieved in terms of securing what was legally correct for three of them ... The fight goes on to get the other five out."
Seven of the suspects were sentenced on 9 August to prison terms ranging between three and seven years. The three released yesterday - Shahzad Nabi, 20, Ayaz Hussein, 26, both from Birmingham, and Ghulam Hussein, 25, from Luton in Bedfordshire - had been sentenced to time served. Ghulam Hussein was released earlier because he was ill, but was ordered to stay in the country until the trial.
On Saturday, a Yemeni court rejected appeals against the convictions from both the prosecution and defence, saying they had been filed after the legal time period had expired. But the judge also ruled that the two men who had been sentenced to time served and were still in jail should be released. The remaining men now have 40 days to appeal against this latest ruling to the Supreme Court.
The 10 men, all of Pakistani or Arab origin, were arrested after last December's kidnapping of 16 Western tourists in Yemen, an incident in which four of the tourists were killed during a rescue attempt by Yemeni troops. All maintained their innocence and said that they had been tortured into giving false confessions.
The men were alleged to have been sent to Yemen by Abu Hamza, a radical cleric based in London, and to have linked up with the Islamic militant Zen al-Abidine al-Mihdar, who was sentenced to death in May for his part in the kidnapping of the Western tourists.
Hamza's 17-year-old son Mohamed Kamel received three years. Malek Nasser, 26, from Birmingham, and Londoner Mohsen Gailan, 18, the stepson of Abu Hamza, both received seven years. Shahid Butt, 33, and Sarmad Ahmed, 21, both from Birmingham, were jailed for five years.
Prosecutors claimed a cache of weapons and communications equipment was discovered in their possession. The defendants said they had gone to Yemen to improve their Arabic and study the Koran.
Ghulam Hussein's twin sister, Nasreen, said last night: "I am very happy that he is coming home. I am waiting for his phone call. Things have changed so much through all this, first it is one thing, then something else, that I won't really believe it until he is here."