"The decision [to release them] follows intensive and complex discussions to address US security concerns ... the four men will be returned in the next few weeks," Straw told parliament on Tuesday.
Feroz Abbasi, Martin Mubanga, Richard Belmar and Moazzam Begg and Australian Mamduh Habib have all been held for three years at the prison camp set up by the US in Cuba in January 2002. The date for their release has not yet been set, but is expected soon.
British police will then consider whether to arrest them under UK terror laws, he added. Straw did not say whether the move was part of a US effort to radically reduce the number of prisoners at the base.
Mental scars cited
Australia's Attorney-General Philip Ruddock was unwilling to comment on what might happen to Habib, a father of four.
However, he said Habib was being sent home at Canberra's request, even though the US still regarded him as an enemy combatant.
Moazzam Begg has been held at
Guantanamo without charges
The US holds about 550 non-US citizens at the Cuban naval base. Only four have ever been charged.
While families of Guantanamo prison camp detainees welcomed news of their sons' imminent release, they emphasised the three-year-ordeal had left mental scars and was far from over.
Azmat Begg, father of British detainee Moazzam Begg, said on Monday that the experience of keeping people in solitary confinement without trial for months on end had to be challenged.
"People who have broken the law of humanity by keeping people for that long in solitary confinement and torturing [them] ... should also be taken account of."
He added that "if there is a proper case, he should be tried and, if he has done something wrong, he should be punished".
Begg pointed out that not only had his son never been charged, but that five other British detainees previously returned to UK had to be released immediately for lack of evidence.
Louise Christian, lawyer for two of the five, said the families feared they would have been seriously mentally damaged by the experience.
"We know they have been tortured and ill-treated. So I think the UK authorities should give serious consideration as to whether it is a disproportionate response to arrest them after they have spent three years being locked up in cages," she said.
"The UK authorities should give serious consideration as to whether it is a disproportionate response to arrest them after they have spent three years being locked up in cages"
She said the families were considering claiming compensation for the trauma. Both Mubanga and Begg have said they were shackled and tortured in the camp although US authorities have dismissed their allegations.
A spokesman for rights watchdog Amnesty International, James Dyson, said London "should make sure all allegations of torture and mistreatment at Guantanamo are investigated".
"We would expect that whatever deal was agreed between the UK and US government should be a straightforward deal with no conditionality about it," he said.
Experts say the five could not get a fair trial after their much-publicised detentions at Guantanamo and that any evidence obtained from the prison camp would be inadmissible.
And in a Pentagon statement released on Tuesday, Washington insisted indefinite detention without trial was legal.
"These detainees are enemy combatants who had been detained by the United States in accordance with the laws of war and US law," the Pentagon said.
"The governments of the United Kingdom ... have accepted responsibility for these individuals and will work to prevent them from engaging in or otherwise supporting terrorist activities in the future."